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Politecnico di MilanoDepartment of Mechanical Engineering
Doctoral Programme In Mechanical Engineering
INTEGRATED QUALITY AND PRODUCTION
LOGISTIC PERFORMANCE MODELING FOR
SELECTIVE AND ADAPTIVE ASSEMBLY
SYSTEMS
Doctoral Dissertation of:
Dariush Ebrahimi Azarbayejan
Supervisors:
Prof. Marcello COLLEDANI
Tutor:
Prof. Roberto VIGANO’
The Chair of the Doctoral Program:
Prof. Bianca Maria COLOSIMO
2014 - XXVI Cycle
Abstract
Selective and adaptive assembly systems are found in several manufactur-
ing contexts, above all automotive and mechanical components manufac-
turing, where the tolerances imposed on the assembled product key fea-
ture are much tighter than the tolerances imposed on the sub-assemblies
key features. In addition, due to the increasing pressure on high precision
manufacturing and the development of on-line measurement technologies,
selective and adaptive assembly systems have attracted increasing interest
in emerging sectors such as micro-production, biomedical and e-mobility
industries. In fact, selective and adaptive assembly system consists in mea-
suring the key quality characteristics of each sub-assembly and classifying
the sub-assemblies into buffers according to the measurement outcome.
In this thesis, a new analytical method is developed that allows predicting
the integrated quality and production logistics performance of the selec-
tive and adaptive assembly systems. The accuracy of the method is shown
by comparison of the results with that of simulation. The method is used
to derive insights on the behavior of these complex class of manufactur-
ing systems. For instance, the effect of total buffer space and the effect
of number of quality classes on the performance measures of the system
is explored and analyzed. The results show that improved performance is
achieved towards existing solutions, which deal only with quality aspects.
For example, we showed that by employing selective and adaptive assembly
systems, high precision assemblies can be produced from low precision sub-
assemblies with the required production rate, at the cost of increasing the
complexity of the system logistics, the work-in-progress and of decreasing
the total production rate of the system.
In addition, we have applied the process adaptation in the manufacturing
process in order to reduce the discard rate of sub-assemblies in selective and
adaptive assembly systems. The proposed method is modeled within the
analytical performance measurement framework of the selective assembly
systems. Moreover, new flow control policies are proposed and analyzed
in order to reduce the discard rate of the selective assembly system where
process adaptation in the manufacturing process is infeasible.
Finally, the industrial benefits are shown by means of applications to two
real manufacturing context. First, producing electrical drives in Bosch com-
pany and then remote laser welding application for body-in-white produc-
tion in Jaguar and Land Rover company. We shown that the effective
throughput is remarkably increased by applying the selective assembly sys-
tem, although the total throughput is decreased. Moreover, in the first case
we have shown that the benefits of introducing more quality classes into
the selective assembly system are more visible as the tolerance on the key
feature of the final assembly is tightened.
iv
To my father,
Dr. Habib Ebrahimi Azarbayejan,
and my mother,
Maryam Banoo Saraydarchi Toussi
Acknowledgements
The contributions of many different people, in their different ways, have
made this thesis possible. I would like to extend my appreciation especially
to the following.
I would like to express my sincere gratitude to my supervisor Dr.Marcello
Colledani for the support of my Ph.D study and research, for his moti-
vation, patience, and for providing me his great knowledge and experience.
His good advice always helped me to keep working when I faced the most
difficult obstacles of my research.
I would like to thank to Prof. Tullio Tolio, Prof. Bianca Colosimo, Prof.
Barbara Previtali and Prof. Giovanni Moroni for their insightful comments,
and the wonderful lessons through my Ph.D courses.
I would like to thank to all my colleagues in the Mechanical Engineer-
ing Department, who made my PhD program enjoyable and convenient. I
would like to thank especially to Anteneh Yemane, Andrea Ratti, Chanaka
Senanayake, Wahyudin Permana and Danial Ramin for their great accom-
pany and providing me their useful insights to my research. Besides my
colleagues, I would like to thank to our coordinator Dr.Sivia Barattieri for
her patience and her wonderful attitude to help me during my PhD program.
I am most grateful to my parents, Habib Ebrahimi Azarbayejan and Maryam
banoo Saraydarchi Toussi for their love and their spiritual support through-
out my life. Also, I would like to thank my sister, Tannaz, for her motiva-
tional and inspirational comments as well as her educational advice.
Last but not the least I would like to thank my family and my dear friends:
Mehdi Motesharei, Reza Motesharei, Toktam Saraydarchi, Navid Rezaee
and Sadegh Riyahi for their support and being the encouragement through
my PhD program.
Contents
List of Figures vii
List of Tables xi
1 Introduction 1
1.1 Current Manufacturing Environment and Systematic Challenges in As-
sembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Assembly Quality Improvement Policies . . . . . . . . . . . . . . . . . . 2
1.2.1 Traditional Assembly to meet the required assemble quality: The
sub-assembly level strategy . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Selective Assembly to meet the required assemble quality: The
assembly process level strategy . . . . . . . . . . . . . . . . . . . 3
1.3 Selective Assembly Systems . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Selective Assembly Applications . . . . . . . . . . . . . . . . . . 5
1.4 Selective Assembly Systems Literature Review . . . . . . . . . . . . . . 7
1.5 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Theoretical Background: Performance Evaluation Methods In Man-
ufacturing Systems 11
2.1 Importance Of Manufacturing Systems Performance Evaluation . . . . . 11
2.1.1 Simulations Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.1.2 Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Review of analytical models: Exact Methods and Approximate Methods 13
2.2.1 Exact Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Approximate Methods . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.3 Traditional Assembly Systems Performance Measurement . . . . 18
iii
CONTENTS
3 Selective Assembly System Conventions, System Description and An-
alytical Performance Evaluation Methodology 21
3.1 Mechanical Assemblies Conventions . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Manufacturing System Conventions . . . . . . . . . . . . . . . . 23
3.2 Selective Assembly System Description . . . . . . . . . . . . . . . . . . . 24
3.2.1 Manufacturing machines and inspection stations . . . . . . . . . 25
3.2.2 The Assembly Machine . . . . . . . . . . . . . . . . . . . . . . . 27
3.2.3 Modeling Assumptions and Notations . . . . . . . . . . . . . . . 30
3.2.4 Deadlock States . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 System Performance Measures . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Two-level Decomposition Approach . . . . . . . . . . . . . . . . . . . . . 35
3.4.1 Buffer Level Decomposition . . . . . . . . . . . . . . . . . . . . . 38
3.4.1.1 Upstream Pseudo-machine . . . . . . . . . . . . . . . . 38
3.4.1.2 Downstream Pseudo-machine . . . . . . . . . . . . . . . 39
3.4.1.3 Building Block Analysis . . . . . . . . . . . . . . . . . . 40
3.4.1.4 Inputs to the MLD . . . . . . . . . . . . . . . . . . . . 41
3.4.2 Machine Level Decomposition . . . . . . . . . . . . . . . . . . . . 41
3.4.2.1 Sub-assembly Manufacturing Machines: Mx and My . . 41
3.4.2.2 Assembly Machine . . . . . . . . . . . . . . . . . . . . . 49
3.4.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4.4 System Performance Measures . . . . . . . . . . . . . . . . . . . 61
3.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5.1 Accuracy testing . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Selective Assembly System Analysis 69
4.1 Selective Assembly System Behavior . . . . . . . . . . . . . . . . . . . . 69
4.2 The Effect of More Quality Classes for Selective Assembly Systems . . . 73
5 Selective and Adaptive Assembly Systems 81
5.1 Selective and Adaptive Assembly Systems Definition . . . . . . . . . . . 81
5.1.1 Process Adaptability Approach To Reduce The Discard Rate:
Analytical Approach . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.1.1.1 Sub-assembly Manufacturing Machine My . . . . . . . . 85
iv
CONTENTS
5.1.1.2 The Effect of Process Adaptation On the System Per-
formance . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.2 The Optimal Process Shift Design in Selective and Adaptive As-
sembly Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.1.2.1 Modeling Assumptions . . . . . . . . . . . . . . . . . . 91
5.1.2.2 Matching Probability Evaluation Method . . . . . . . . 93
5.1.2.3 Shift Design Optimization . . . . . . . . . . . . . . . . 94
5.1.3 The Effect of Optimal Process Adaptation on the System Perfor-
mance Applying Simulation Model . . . . . . . . . . . . . . . . . 100
6 Deadlock State Correction Policies 109
6.1 Assembly Level Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Sub-assembly Manufacturing Level Policies . . . . . . . . . . . . . . . . 112
6.3 Numerical results of the deadlock correction policies . . . . . . . . . . . 114
6.3.1 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7 Selective Assembly Application in Electrical Engine Production: Bosch
Case 135
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
7.2 Bosch Electrical Engine manufacturing system description . . . . . . . . 136
7.2.1 Manufacturing Stages . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2.2 Modeling Approach . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.2.3 Characterization of the quality parameters . . . . . . . . . . . . 142
7.3 New Configurations For Rotor Manufacturing Line . . . . . . . . . . . . 143
7.3.1 Selective assembly with two quality classes connected to two buffers.143
7.3.2 Selective assembly with four quality classes connected to four
buffers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.3.3 Selective assembly with six quality classes connected to six buffers.149
7.3.4 Selective assembly with eight quality classes connected to eight
buffers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
7.3.5 Comparison of the four analyzed configurations . . . . . . . . . . 150
7.4 The Effect of Final Assembly Key Characteristic Tolerance Tightening
on The Effective Throughput . . . . . . . . . . . . . . . . . . . . . . . . 157
7.4.1 Experiments Results . . . . . . . . . . . . . . . . . . . . . . . . . 158
v
CONTENTS
8 Selective Assembly Application in Automotive Industry: Door As-
sembly in Jaguar and Land Rover Company 163
8.1 JLR Door Manufacturing System Description . . . . . . . . . . . . . . . 164
8.2 The New Configuration of Assembly System: Application of Remote
Laser Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
8.3 The New Configuration of Hybrid System including Selective Assembly
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9 Conclusion 187
References 191
vi
List of Figures
1.1 System Description of Selective Assembly System. . . . . . . . . . . . . 4
1.2 Piston Cylinder Assembly, where the clearance is the assembly key char-
acteristics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Application of Selective Assembly Systems in remote laser welding. . . . 6
2.1 Decomposition Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Assembly System Decomposition Example. . . . . . . . . . . . . . . . . 19
3.1 Selective Assembly System Topology . . . . . . . . . . . . . . . . . . . 25
3.2 Machine X system topology. . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Assembly Machine System Topology. . . . . . . . . . . . . . . . . . . . . 28
3.4 Deadlock state 1 for the Selective Assembly with two quality classes. . . 32
3.5 Deadlock state 2 for the Selective Assembly with two quality classes. . . 32
3.6 Two level decomposition approach for selective assembly systems. . . . 36
3.7 Buffer Level Decomposition for lx(1). . . . . . . . . . . . . . . . . . . . . 42
3.8 Markov model representing Mx characteristics. . . . . . . . . . . . . . . 43
3.9 State transition diagram for upstream Pseudo machine L(x1). . . . . . . 44
3.10 Markov model representing Ma characteristics. . . . . . . . . . . . . . . 52
3.11 State transition diagram for downstream Pseudo machine l(x1). . . . . . 52
4.1 Total throughput behavior as the total buffer space increases. . . . . . 71
4.2 Effective throughput behavior as the total buffer space increases. . . . . 72
4.3 WIP behavior as the total buffer size increases. . . . . . . . . . . . . . . 73
4.4 Total TH behavior as the number of quality classes increases. . . . . . . 76
4.5 The effective throughput behavior as the number of quality classes in-
creases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
vii
LIST OF FIGURES
4.6 System Yield behavior as the number of quality classes increases. . . . . 79
5.1 Three shift policy for adaptive production systems. . . . . . . . . . . . . 83
5.2 Markov model characterizing the Machine Y, My, with process adjust-
ments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.3 Pseudo machine state transition diagram. . . . . . . . . . . . . . . . . . 88
5.4 Effect of Shifts on System performance. . . . . . . . . . . . . . . . . . . 90
5.5 Five symmetric shifts of process mean for Y. . . . . . . . . . . . . . . . 92
5.6 Block Diagram for Problme 2. . . . . . . . . . . . . . . . . . . . . . . . . 95
5.7 Matching probability as a function of the number of shifts - Case 1. . . 97
5.8 Matching probability as a function of the number of shifts - Case 2. . . 100
5.9 Schematic representation of selective and adaptive assembly systems for
the experiments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.10 Observed throughput under different shifts designs for case 1. . . . . . . 106
5.11 Observed WIP under different shifts designs for case 1. . . . . . . . . . . 106
5.12 Observed throughput under different shifts designs for case 2. . . . . . . 107
5.13 Observed WIP under different shifts designs for case 2. . . . . . . . . . . 107
6.1 Assembly Level Policies: Reactive Class Mix. . . . . . . . . . . . . . . . 110
6.2 Assembly level policies: Preventive Class Mix. . . . . . . . . . . . . . . . 111
6.3 Assembly Level Policy: Buffer Level Dependent. . . . . . . . . . . . . . 112
6.4 Manufacturing machine level policies: System Level Discard. . . . . . . 113
6.5 Manufacturing machine level policies : System Level Discard 1 Machine. 114
6.6 Experiment1: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.7 Experiment2: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.8 Experiment3: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.9 Experiment4: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.10 Experiment5: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
viii
LIST OF FIGURES
6.11 Experiment6: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.12 Experiment1: The discard rate for proposed deadlock correction policies. 127
6.13 Experiment2: The discard rate for proposed deadlock correction policies .128
6.14 Experiment3: The discard rate for proposed deadlock correction policies. 129
6.15 Experiment4: The discard rate for proposed deadlock correction policies. 130
6.16 Experiment5: Effective throughput behavior for proposed deadlock cor-
rection policies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.17 Experiment6: The discard rate for proposed deadlock correction policies. 132
7.1 Integrated Mototr Generator (Bosch). . . . . . . . . . . . . . . . . . . . 137
7.2 Schema of Current Manufacturing System. . . . . . . . . . . . . . . . . . 138
7.3 Approximation of the original Bosch layout with a multistage process-
chain model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
7.4 Selective Assembly of stacks: schematic view. . . . . . . . . . . . . . . . 144
7.5 Proposed configuration: Selective assembly system with two classes. . . 145
7.6 Distribution of the magnetic flux intensity of the coupled stacks applying
the selective assembly with two quality classes and normal assembly
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.7 Proposed configuration: Selective assembly system with four classes. . . 147
7.8 Distribution of the magnetic flux intensity of the coupled stacks applying
the selective assembly with four quality classes and normal assembly
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.9 Distribution of the magnetic flux intensity of the coupled stacks apply-
ing the selective assembly with six quality classes and normal assembly
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
7.10 Proposed configuration: Selective assembly system with six classes. . . . 150
7.11 Proposed configuration: Selective assembly system with eight classes. . . 151
7.12 Distribution of the magnetic flux intensity of the coupled stacks applying
the selective assembly with eight quality classes and normal assembly
strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
7.13 Reduction of variance with increasing number of quality classes. . . . . 153
7.14 Throughput total as the number of quality class increases. . . . . . . . . 155
ix
LIST OF FIGURES
7.15 Discard Rate as the number of quality class increases. . . . . . . . . . . 156
7.16 System Yield as the number of quality class increases. . . . . . . . . . . 157
7.17 Effective Throughput as the number of quality class increases. . . . . . . 158
7.18 Effect of tightening the tolerance on TH Eff. . . . . . . . . . . . . . . . 161
8.1 Current Assembly Sequence of Front door for model. . . . . . . . . . . 165
8.2 Precedence Diagram for the front door assembly line for the current
configuration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.3 Schematic layout of current manufacturing system for assembly line of
right and left front door (identical systems). . . . . . . . . . . . . . . . 167
8.4 Current manufacturing system model of the door assembly system. . . . 168
8.5 Graphical operation synthetic description . . . . . . . . . . . . . . . . . 169
8.6 Precedence Diagram for the front door assembly line for the new config-
uration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
8.7 The layout representing the new hybrid configuration. . . . . . . . . . . 178
8.8 Proposed configuration for left front and right front door including RLW
station with normal assembly system, focusing on the right front door. 182
8.9 Proposed configuration including the selective assembly system of two
classes for right side front door. . . . . . . . . . . . . . . . . . . . . . . . 183
8.10 Proposed configuration including the selective assembly system of three
classes for right side front door. . . . . . . . . . . . . . . . . . . . . . . 185
x
List of Tables
3.1 behavior of machine Mx. ”B” denotes blocking states, ”W” denotes
operational states, and ”R” denotes down states. . . . . . . . . . . . . . 46
3.2 Behavior of machine Ma. ”S” denotes starvation states, ”W” denotes
operational states, and ”R” denotes down states. . . . . . . . . . . . . . 50
3.3 Summary of the adopted parameters. . . . . . . . . . . . . . . . . . . . . 63
3.4 Range of variable parameters of accuracy test of analytical tool. . . . . . 63
3.5 experimental results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.1 Summary of the adopted parameters for more quality classes test. . . . 74
4.2 Partitioning limits for equal probability scheme. . . . . . . . . . . . . . . 75
4.3 Performance measures as the number number of quality classes increases. 77
5.1 Behavior of machine My. ”B” denotes blocking states, ”W” denotes
operational states, and ”R” denotes down states. . . . . . . . . . . . . 86
5.2 Summary of the adopted parameters. . . . . . . . . . . . . . . . . . . . . 90
5.3 Sample case data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4 Maximum matching probability for a given number of shifts in Case 1. . 97
5.5 Binning and probabilities for Case 1, without process adaptation. . . . . 98
5.6 Details results in the application of three alternative methods for Case 1. 99
5.7 Maximum matching probability for a given number of shifts in Case 2. . 100
5.8 Binning and probabilities for Case 2, without process adaptation. . . . . 101
5.9 Details results in the application of three alternative methods for Case 2. 102
5.10 Case 1: Simulated total throughput and WIP for different shifts designs
(3* denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).105
xi
LIST OF TABLES
5.11 Case 2: Simulated total throughput and WIP for different shifts designs
(3* denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).108
6.1 Experimental plan for deadlock correction policies. . . . . . . . . . . . . 116
6.2 Performance measures results for experiment 1. . . . . . . . . . . . . . . 117
6.3 Performance measures results for experiment 2. . . . . . . . . . . . . . . 117
6.4 Performance measures results for experiment 3. . . . . . . . . . . . . . . 118
6.5 Performance measures results for experiment 4. . . . . . . . . . . . . . . 118
6.6 Performance measures results for experiment 5. . . . . . . . . . . . . . . 119
6.7 Performance measures results for experiment 6. . . . . . . . . . . . . . . 119
7.1 Mean time to failure, mean time to repair and cycle time of the machines. 142
7.2 Capacity of each buffer in the current manufacturing system[number of
stacks]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.3 Equal probability partitioning scheme for four quality classes. . . . . . . 147
7.4 Equal probability partitioning scheme for six quality classes. . . . . . . . 150
7.5 Equal probability partitioning scheme for eight quality classes. . . . . . 152
7.6 Performance measures of the proposed Selective Assembly configurations. 154
7.7 Tested Tolerance Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
7.8 Performance Measures for the tolerance limit divided by 2 (T/2). . . . . 160
7.9 Performance Measures for the tolerance limit divided by 4 (T/4). . . . . 160
7.10 Performance Measures for the tolerance limit divided by 6 (T/6). . . . . 160
8.1 Current Manufacturing System Station Description. . . . . . . . . . . . 172
8.2 Summary of parameters of the current manufacturing system, adopted
for analytical performance measurement method. . . . . . . . . . . . . . 174
8.3 Summary of parameters of the proposed manufacturing system, adopted
for analytical performance measurement method . . . . . . . . . . . . . 177
8.4 Operation Synthetic of the new hybrid proposal including both RLW
and RSW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
8.5 Performance measures of the proposed manufacturing system with no-
selective assembly system. . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.6 Performance measures of the proposed manufacturing system for selec-
tive assembly system of 2 and 3 quality classes. . . . . . . . . . . . . . . 186
xii
1
Introduction
1.1 Current Manufacturing Environment and Systematic
Challenges in Assembly
In the current manufacturing environment, we observe an increasing complexity of the
products design and their applications. In addition, day by day products contains more
kinds of technologies, including electronics, mechanics and optics. For example, looking
at the new product such as cellphones and cameras or laptops, we can observe the fact
that they are becoming more performing and also they are being made in wide vari-
ety of versions, which means recognition of customers taste that is crucial to survive
for industries. Additionally, complexity of the new products and level of technology
that they required, push companies towards more precision in assembly process as well
as upstream manufacturing phases. However, variation is the physical results of any
manufacturing processes: components and assemblies are different from what we want
them to be although they are suppose to be identical. As a result, the actual value of
each component’s key characteristic will deviate from the desired value. In fact, in the
assembly process, manufactured sub-assemblies variation will accumulate via chains of
frames that pass through the sub-assemblies. The net result of these variations gener-
ates the final assembled product key characteristic variations. If the generated variation
on the key characteristic of the final product becomes more than its defined tolerance
limits the product is identified as non-conforming and it will be scraped.
This must be noticed that, customers request for a lower price and higher quality leads
1
1. INTRODUCTION
to the fact that only those companies who provide lower price and higher quality would
survive. However, complexity of new designed products acts conversely to lowering the
price and improving the quality. Therefore, it is crucial to propose an efficient approach
to improve the quality of the final assembled product, while reducing the production
cost to meet the customers requirements.
1.2 Assembly Quality Improvement Policies
Final assembly is the moment of truth, where all the upstream processes from design
and logistic to engineering and manufacturing with the aim of creating an object to
function specific task, are brought together. In the other words, an assembly process
is more than joining parts together. In fact, people and companies who are involved in
any stage of product development are forced to work together closely in order to obtain
the good assembled product. Otherwise the final product never become successful in
the final integration, i.e., the assembly process. Naturally, the upstream processes such
as manufacturing process are influenced strongly by assembly process through imposing
the tolerances on key characteristics features of any single sub-assembly. Although the
assembly is an important and influential process for the whole company, in this thesis
we focus on the link between the assembly process and its impact on the system level
domain, specifically in terms of final assembly quality and logistics performance of the
assembly systems.
1.2.1 Traditional Assembly to meet the required assemble quality:
The sub-assembly level strategy
Considering the high level of quality and complexity of the assembled product, deter-
mining the limits of variations for each sub-assemblies through tolerance synthesis seeks
to put the hard bounds for tolerance limits of each sub-assemblies. In the sub-assembly
level strategy, imposing these hard bounds on the components’ tolerance is considered
as an approach to meet the required quality of assembled products, although increasing
the whole manufacturing time and cost. However, this approach can be inefficient since
for many manufacturing technologies, the possibility of processing the components with
2
1.3. SELECTIVE ASSEMBLY SYSTEMS
lower tolerances is limited due to inherent process capability constraints. Therefore,
improving the quality of each sub assemblies could cause the expenditure cost due to
technology improvement of the sub-assembly’s manufacturing processes. If the com-
pany’s expenditure cost is non-affordable for the company, hard bounded tolerance
limits on the sub-assemblies wide variation cause increasing level of non-conforming
products. In both cases, companies are under the huge cost pressure to be able to
produce sub-assemblies that are interchangeably conforming for assembly.
1.2.2 Selective Assembly to meet the required assemble quality: The
assembly process level strategy
The concept of selective assembly represents a formal approach to obtain the high pre-
cision assembled products from relatively low precision sub-assemblies. Therefore, this
approach allows to overcome the technological limitation which is imposed by manu-
facturing systems trough coordination in the assembly process. As a matter of fact, the
advances in sensor technology have provided the possibility of rapidly inspecting several
product characteristics in a short time, with high accuracy and in-line. Selective as-
sembly consist in performing in-line inspection and in partitioning the sub-assemblies
into quality classes, depending on the specific outcome of the measurement process.
Therefore, only the matched sub-assemblies form the compliant buffers are assembled.
In the selective assembly the sub-assemblies are treated as an individuals rather than
statistical identical members of an assemble. Selective Assembly is a system level
approach which is proposed when process variability is too large which cause the pro-
duction of sub-assemblies with high variation in their key quality characteristic and it
is not economical to imposed the hard bounds decided by tolerance synthesis.
1.3 Selective Assembly Systems
As shown in Figure 1.1, selective assembly system involves sub-assemblies manufactur-
ing machines, sub-assemblies storage area, and assembly machine. The first stage is the
sub-assemblies manufacturing part of these systems. Machines Mx and My are man-
ufacturing machines and are behaving identically. Mx manufactures the sub-assembly
X and in-line inspection station (showed in red square) measures the key characteristic
3
1. INTRODUCTION
Figure 1.1: System Description of Selective Assembly System.
of the manufactured sub-assembly. The measured sub-assembly is placed in one of the
dedicated buffers according to its key characteristics, which is the second part of selec-
tive assembly systems. Number of buffers for each sub-assembly is equal. Therefore,
each sub-assembly class has its own complaint sub-assembly, to be joint to. For example
buffer B1y contains sub-assemblies to be assemble to sub-assemblies in buffer B1
x. The
assembly machine, selects the compliant sub-assemblies and assembles them. Finally,
the final inspection categorize the conforming and non-conforming final assemblies.
As depicted in Figure 1.1 assembly machine is matching only the compliant sub-
assemblies therefore it is expected to obtain better system yield (fraction of conforming
assembled products). However, classification of the sub-assemblies by manufacturing
machines and matching the complaint sub-assemblies by assembly machine cause strong
complexity in system logistics. As a matter of fact, the selective assembly system trans-
lates a product quality issue into a system logistics issue.
Selective assembly is an expensive strategy and is suggested to be applied when the
alternative strategy, namely making each part accurately enough for interchangeability,
is even more expensive. The main additional cost of selective assembly is the increased
level of logistics complexity which results in the reduced productivity of such a system.
Although the logistic complexity is highly increased in this class of system, but it has
4
1.3. SELECTIVE ASSEMBLY SYSTEMS
Figure 1.2: Piston Cylinder Assembly, where the clearance is the assembly key charac-
teristics.
been practiced in several industries. In the following section we will demonstrate some
of applications of selective assembly systems in industries.
1.3.1 Selective Assembly Applications
In the past, selective assembly is applied to traditional sectors, such as mechanical com-
ponents production as shown in Figure 1.2. For example, consider a piston and cylinder
assembly where the tolerance on the clearance between the two components is narrower
than the dimensional variability of the two sub-assemblies. If the assembly system se-
lects two components randomly from the upstream storage, the clearance could easily
be either too tight or too wide. In both cases, the assembled product is scrapped.
Under the selective assembly logistic, only compliant pre-classified sub-assemblies are
assembled, thus allowing a tighter control of the clearance. In fact, selective assembly
in this particular case suggests matching the smaller piston with smaller cylinder and
larger pistons with larger cylinders.
However, due to the increasing pressure on high precision manufacturing and to the
development of advanced and fast measurement technologies supporting on-line appli-
5
1. INTRODUCTION
Figure 1.3: Application of Selective Assembly Systems in remote laser welding.
cations, selective assembly systems have attracted increasing interest in the last five
years, especially in fast growing sectors such as micro-production Lchte et al. [2012],
in renewable energy equipment production (large parts assembly in windmills, electri-
cal engine assembly in the e-mobility sector), and in the automotive body assembly
Ceglarek and Huang [2007].
For example, selective assembly has been suggested as an effective approach to support
tight dimensional control of part-to-part gap during remote laser welding operations in
the automotive industry FP7-2011-NMP-ICT-FoF [2012]. In this application, a tight
gap control is essential to ensure the high quality of the produced stitch, in terms of
mechanical properties and corrosion resistance. Typically, the gap cannot be smaller
the 0.1mm while processing zinc coated sheet metals. The risk of a smaller gap is
the explosion or ejection of molten weld metal caused by the escape of trapped high
pressurized zinc vapor. Moreover, the gap cannot be larger than 0.3mm. The reason is
the risk of lack of fusion and insufficient penetration of the stitch in the components.
Selective assembly can classify compliant sheet metals after forming in order to have
a homogeneous gap between components during the welding process, contributing to
high quality welding. This requires the inspection-based characterization of the geo-
metrical variation of the metallic sheets. The measured data can be characterized by
statistical modal analysis Ceglarek and Huang [2007]. Figure 1.3 shows the application
of selective assembly systems in the remote laser welding technology.
6
1.4. SELECTIVE ASSEMBLY SYSTEMS LITERATURE REVIEW
Another recent application of selective assembly is found in the production of electrical
engines for the e-mobility sector FoF.NMP.2011-5 [2011]. Electrical engines are ob-
tained by assembling rotor and stator. The rotor is formed by a group of magnetic
stacks. Each stack has a set of magnets mounted on the external surface. The produc-
tion process involves the assembly of the magnets on each stack and the subsequent
magnetization of the entire stack. Then, the stacks are axially assembled to form the
rotor. However, due to the variability of the magnetization process, the magnetic field
intensity of the stacks are highly inhomogeneous, directly affecting the magnetic torque
of the final engine. Therefore, by classifying the stacks according to their field profile
and by selectively assembling the stacks in the rotor it is possible to reduce the variabil-
ity of the magnetic field intensity and to increase the stability of the engine magnetic
torque. We proposed the implementation of the selective assembly system in the cor-
responding manufacturing system of electrical engines production. The final chapter
of this thesis is dedicated to the analysis of the proposed system configuration, which
implies the positive effects of the selective assembly systems comparing to the current
configuration.
1.4 Selective Assembly Systems Literature Review
In the literature, the performance of selective assembly systems has been addressed by
mainly focusing on the effect of the partitioning design (also named sorting policy or
selection policy) on the assembled product quality. Partitioning is often based on two
schemes, i.e. equal width and equal probability partitions. In equal width scheme all
the assembled products can have the clearance within the tolerance limit, because the
sub-assemblies’ partitions have equal width in terms of key characteristic distribution.
However, in the cases that the key characteristic distributions of sub-assemblies are dis-
similar there will be a large number of sub-assemblies waiting for the their compliant
sub-assemblies in partitions (In the literature these sub-assemblies are called surplus
components). In equal probability scheme, sub-assemblies are partitioned into quality
classes with the equal probability for each sub-assembly. In this scheme, in case of
imbalanced key characteristic variation distributions there will be a fraction of rejected
assembled products although the surplus sub-assemblies could be reduced to zero. In
Mease et al. [2004] the authors propose optimal partitioning strategies under several
7
1. INTRODUCTION
loss functions and distribution assumptions, considering situations in which only one
of the components is partitioned as well as situations in which both components are
partitioned. They showed that zero-defect assembly is possible at the cost of drastically
increasing the number of quality classes, thus highly complicating the system logistics.
In [Kannan and Jayabalan, 2001a], an algorithm for minimizing the surplus compo-
nents in selective assembly is developed through defining the new partitioning design
for three sub-assembly assembly system. They showed that the number of partitions
are reduced, the surplus components are considerably minimized while the tolerance
of the final assembly is respected. Fang and Zhang [1995] proposed a partitioning
strategy based on equal probability scheme. They proposed a recursive algorithm to
define the partitioning of the sub-assemblies after the manufacturing within the certain
tolerances.Shun Matsuuraa [2007] provided optimal partitioning methodology under
squared loss errors, taking into consideration the measurement error influence. In Kan-
nan and Jayabalan [2001b],they proposed equal width partitioning scheme in case the
tolerance of clearance is smaller than the difference of three times the standard devi-
ation of the sub-assemblies key characteristics, otherwise equal probability scheme is
proposed. Kannan et al. [2005] provided a method to reduce the number of surplus sub-
assemblies as well as variations in clearance. These studies are typically supported by
statistical methods and do not consider the impact of the sorting policy on production
logistics related performance. Often the better quality of the final assembly is obtained
by increasing of the number of partitions. While at the same time ,more partitions
increase the system logistic complexity. Recently, simulation approach has been used
for predicting the impact of specific adaptation policies (Halubek et al. [2010], Kayasa
and Herrmann [2010]) on the system performance. They have applied the simulation
approach to support planning and control of the adaptable production systems.
These works typically neglect important production logistics features and the realistic
settings of the system, such as finite capacity buffers and unreliable machines. By doing
so, a relevant problem is neglected, i.e. the arising of deadlock states in the system that
need to be handled are avoided. Although selective assembly improves the quality of the
final assembly, but it complicates the logistic of such a systems which cause deteriorating
the productivity. As a matter of fact, an integrated quality and logistic performance
framework and an analytical methodology to support the design of selective assembly
8
1.5. THESIS CONTRIBUTIONS
systems have never been proposed, reducing the potential benefit of these systems in
industry. Considering the integrated quality and productivity framework to analyze
the selective assembly systems, we can answer the important questions like “What
is the impact of the number of partitions on the throughput of conforming assembled
products?” or “How limited buffers impact the system performance”. Otherwise, the
consequent configuration corresponds unbalanced and sub-performing system adopted
in industry.
1.5 Thesis Contributions
In this thesis we focus on developing an integrated framework of quality and produc-
tion logistic performance for selective assembly systems. A new approximate analytical
method for the prediction of the throughput of conforming products, the system yield
and the WIP in these systems is developed for the first time. Also, we proposed a new
deadlock correction policy based on the process adaptability of manufacturing systems.
The proposed method is developed in an analytical method. Several new intelligent
flow control policies based on the observable system state is proposed to improve the
performance of the selective assembly systems. We showed that the proposed policies
outperform the current policies for deadlock avoidance through the developed simula-
tion model.
Finally, we have proposed a new algorithm for optimal design of adaptable manufac-
turing systems that supply the sub-assemblies of selective assembly systems. In this
method we proposed the optimal approach for alternating the process target value to
minimize the surplus components of selective assembly system. The system level effect
of the optimal design of adaptable manufacturing system has been analyzed as well.
9
1. INTRODUCTION
10
2
Theoretical Background:
Performance Evaluation Methods
In Manufacturing Systems
2.1 Importance Of Manufacturing Systems Performance
Evaluation
In this chapter we will review the literature on the performance evaluation tools for
the system-level performance of manufacturing systems. In any manufacturing system
there are many random events that interrupt the production, such as machine failures.
These random events complicate the performance estimation of any manufacturing
systems and cause the unpredictable behavior of these systems. In addition, starvation
and blocking phenomenon caused by the machine failures can propagate through the
line. For example, a machine could remain starved (idle) because one of the upstream
machines is failed and there is no part in upstream buffer, or the machine could become
blocked because one of the downstream machines is failed and there is a downstream
buffer which is full. Often, it is suggested to increase buffers between machines to cover
the randomness of the events, which results in better throughput. However, the storage
space could be very expensive and limited most of the time. Moreover, increasing the
buffers often complicate the logistic systems and practitioners tend to avoid it.
11
2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS
2.1.1 Simulations Models
Simulation models of manufacturing systems are widely used in system engineering
area. Simulation has the advantage of being flexible and is able to model a wide set of
systems, at the desired level of detail. Simulation most negative effect appears when
manufacturing systems need real-time decision makings, since simulation models require
high computational time to obtain statistically reliable results. When uncontrollable
manufacturing events (such as machine failures) happen some decision must be made
in real-time, such as process routing change or alternating the product scheduling for
flexible manufacturing systems. Alden et al. [2006] reported the inefficiency of simula-
tion models for on-line performance evaluation of the manufacturing systems due to the
long model creation time as well as complicated validation process. Simulation models
are generally suggested as an off-line tool to be used to evaluate the performance of
manufacturing systems and identify existing improvement possibilities. Application of
simulation models adopted for performance evaluation of manufacturing systems can
be found in [Bley et al., 1997, Phillis et al., 1997].
2.1.2 Analytical Models
Analytical models, tends to provide us with deeper understanding of the system and
they are usually much faster than the simulation models. The analytical model of
an assembly line can be imbedded in an optimization algorithm. The optimization
algorithm usually maximizes the throughput by running the analytical model several
times with different system characteristics and it takes few seconds to run these models.
In this way, analytical models can be applied to design manufacturing lines. Simulation
model could be imbedded to the optimization algorithm as well but it takes much more
time comparing to analytical models.
In this thesis we use both types of models. First, we developed a new an analytical
method to estimate the system performance of the selective assembly system. Then in
order to approve the precision of analytical method results, we compared several cases
to the developed simulation model.
12
2.2. REVIEW OF ANALYTICAL MODELS: EXACT METHODS ANDAPPROXIMATE METHODS
2.2 Review of analytical models: Exact Methods and Ap-
proximate Methods
In the literature there are several analytical methods which are introduced to help
manufacturing system engineers estimate the performance of complex systems. We
have differentiated all the analytical methods into two main methods that we review
here, exact analytical methods and approximate analytical methods.
2.2.1 Exact Methods
The exact models are better than the approximation method for cases that fit the real
system closely. In fact, in the approximate methods the exact models are the essential
part of solution due to the rapid solution.
In this section, we review the exact solutions of two-machine transfer lines with
unreliable machines and finite buffers. These systems are modeled as Markov processes
with discrete states and continuous times, as well as Markov processes with discrete
states and discrete times, and as Markov processes with mixed states and continuous
times.Buzacott, 1972 Buzacott [1972] describes a two-machine model with identical
unreliable machines and buffer in middle. Implicitly, he assumed that Both the opera-
tion times and repair times are geometrically distributed.Gershwin and Berman [1981]
investigated the two-machine system in which processing times, times to failure, and
times to repair are all exponentially distributed. They study the two-machine line when
two machines are different.Berman [1982] generalizes the Gershwin and Berman [1981]
considering the processing times to have Erlang distributions.
Buzacott [1967] and Buzacott [1969] proposed an exact method for two-machine sys-
tems when both the failure and the repair processes are geometric or deterministic. He
assumed that the probability that two events happen during the same cycle is negligi-
ble.Artamonov [1977] proposed a method to solve a two-machine line with deterministic
processing time and geometric repair and failure times, without considering the Buza-
cott [1967] and Buzacott [1969] assumption (probability that two events happen during
the same cycle is negligible). The method proposed in Gershwin [1994] (which itself
was a modification of Buzacott [1967]) is extended in Tolio et al. [2002] for unreliable
machines with multiple failure modes. They showed that approximating the failure
13
2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS
modes into a single failure mode which is proposed in Gershwin [1994] overestimated
the production rate of the two machine systems. Gershwin and Schiek [1983] extended
the analytic solution of the deterministic two-machine model of Gershwin [1994] to
three machines. To do this, they had to extend the analysis of internal states and the
analysis of boundary states, which is complicated. A boundary state is characterized
by a state where at least one of the buffers is on the boundary. The resulting tech-
nique was slow and practical only for small buffers. Considering the exact method of
performance analysis, the number of states of the Markov chains grows very fast with
the number of machines, the buffer capacities, and the number of phases of the dis-
tributions. Consequently, only models of limited sizes and with limiting assumptions
can be solved with the exact solutions. In the next section therefore we discuss the
main achievement of the approximate analytical methods to evaluate the performance
of longer manufacturing lines.
2.2.2 Approximate Methods
It comes into view that exact solutions of two-machine flow lines are available for a
both reliable machine and unreliable machines. However, it appears very difficult to
expect to obtain exact solutions of flow lines with more machines. Even the researches
on three-machine lines shows models that are too limited to be applicable, or they are
subject to numerical problems. Therefore, applying the approximate methods is the
only feasible alternative.
Several authors have developed approximation methods, which they call them ag-
gregation methods. The basic idea of aggregation is to substitute a two-machine-one-
buffer sub-system by a single equivalent machine. The equivalent machines has the
same throughput in isolation as the two-machine-one-buffer sub-system. Thus, an ag-
gregation method for analyzing a line with K machines consists in applying K-1 single
aggregation steps in forward and backwards. Performance measures such as through-
put rate of the system can be obtained when the algorithm converges.
Aggregation methods investigated mainly by Meerkov for Bernoulli, geometric and ex-
ponential machine reliability models, as mentioned in Li et al. [15 July 2009]. The main
advantage of the Meerkov aggregation method is that all the aggregation procedures
have been analytically proved to be convergent. In addition, he has studied several
14
2.2. REVIEW OF ANALYTICAL MODELS: EXACT METHODS ANDAPPROXIMATE METHODS
system properties such as bottleneck analysis. Also, Li [2004] and Li and Meerkov
[2003] worked on aggregation methods to estimate the approximate performance of
manufacturing lines.
An alternative approximation method is decomposition which has been applied in a
wide variety of manufacturing system performance evaluation analysis. The idea is to
decompose the original manufacturing model into the set of smaller subsystems which
are easier to analyze. As mentioned in Dallery and Gershwin [1992], each decomposi-
tion method is developed through three steps: (1) characterizing the subsystems; (2)
developing a set of equations that derive the unknown parameters of each subsystem;
and (3) developing an algorithm to solve these equations. First, the original system
must be decomposed into subsystems and then each subsystem must be characterized.
The subsystems must have exact solutions. In the second step relationships between
quantities referring to different subsystems will be established so that the parameters
of each subsystem can be derived from the parameters and performance measures of
other subsystems. In general, the decomposition methods decompose a K-machine
manufacturing system (involving flow lines or any complex architecture) into a set of
K-1 subsystems, each subsystem being associated with the buffer of the original manu-
facturing system. Practically, decomposition methods are approximations because (1)
the decomposed subsystems are simpler than the whole system, and so cannot cap-
ture the same behavior properly; and (2) some of the developed equations applied to
determine the parameters can be approximate. In decomposition methods, there is
an important trade-off between complexity and accuracy. Of course, a more complex
characterization of the subsystems will lead to a better approximation of the behavior
of the original system and, therefore, to more accurate results. However, obtaining the
more accurate solution of subsystems will also be more complex and, since each sub-
system is usually solved in iterative algorithms, the overall computational complexity
become greater.
Decomposition methods have been developed either for flow lines with reliable ma-
chines or for flow lines with unreliable machines. In this thesis we have considered
the two-machine one buffer line for each decomposed subsystem and which is named
building block. Each building block is associated with a buffer of the original line. Let
L denote the original line and let L(i, i+ 1) denote the building block associated with
15
2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS
Figure 2.1: Decomposition Method.
buffer B(i, i + 1). Furthermore, we use superscripts u and d to refer to objects and
parameters of the upstream and downstream machines. Machine Mu(i, i + 1) is the
upstream machine of the building block L(i, i + 1), and Md(i, i + 1) represents the
downstream machine, as graphically depicted in the 2.1.
Note that machine Md(i − 1, i) in line L(i − 1, i) and machine Mu, (i, i + 1) in line
L(i, i + 1) correspond to machine Mi of the original system. It is assumed that the
capacity of the buffer of each building block is the same as that of the corresponding
buffer of the original system.
The basic idea of decomposition is to characterize the upstream and downstream ma-
chines for each building block L(i, i + 1) in such a way that the material through its
buffer behaves close to the behavior of material in buffer B(i,i+1) in the original system.
That is, an observer in the buffer of line L(i, i+1) would see virtually the same arrivals
and departures, starvation and blocking, and buffer level dynamics as an observer in the
buffer of the original system. Exact solutions of the building blocks can be obtained, as
described earlier. The details of the decomposition method can be found in Gershwin
[1987], Choonga and Gershwin [1987], DALLERY et al. [1988] and DALLERY et al.
16
2.2. REVIEW OF ANALYTICAL MODELS: EXACT METHODS ANDAPPROXIMATE METHODS
[1989].
Wide variety of analytical performance evaluation method have been developed by ap-
plying the the decomposition methods. Analytical performance evaluation methods of
More complicated manufacturing systems have been proposed by extending and improv-
ing the decomposition method. A set of new decomposition equations are developed in
Gershwin and Burman [2000] to evaluate the assembly/disassemble systems. The pro-
posed equations cover the complex propagation of blocking and starvation probabilities
along the line. In Colledani et al. [2005] and Colledani et al. [2208] multiple produc-
tion manufacturing systems have been analyzed. In order to apply the decomposition
method a two-machine line dedicated to each product type have been generated. In
Colledani et al. [2005] Markovian analysis of the behavior of the flexible machine pro-
ducing two part types is performed. The same class of manufacturing systems of multi-
ple part type has been studied in Jang and Gershwin [2007] while they have proposed an
exact method for a new type of two machine systems. An analytical performance evalu-
ation method to analyze the continuous flow manufacturing systems when machines are
characterized by general Markovian fluid models is proposed in Colledani and T.Tolio
[2011]. They have proposed a set of new decomposition equations to capture the prop-
agation effects of partial and complete blocking and starvation phenomena throughout
the system. In Colledani and T.Tolio [2005] proposed an approximate analytical ap-
proach based on decomposition method for modeling and evaluating the performance
of manufacturing systems involving split and merge of material flow, multiple product
systems, assembly/disassembly manufacturing systems when buffer capacity is finite.
Some other methods have applied the decomposition method for developing perfor-
mance evaluation method of manufacturing systems including quality aspects. Tem-
pelmeier and Burger [2001] proposed a decomposition method for the performance
evaluation of multi-stage production lines in which the no-conforming parts are scraped
by the system. Helber [2000] proposed a new decomposition method for performance
evaluation of manufacturing systems with split of material flow for rework and scrape.
In Gershwin and J.Kim [2005] they have analyzed the performance of manufacturing
systems monitored by Jikoda practice of stopping the manufacturing line as soon as
non-conformists are identified. The authors proposed a method to characterize the
17
2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS
manufacturing machines with a discrete state-continues time Markov chain to observe
the machine states while machine is operating the good parts, machine is operating
bad parts and finally states in which machine is not working. They have applied the
decomposition technique to develop the performance evaluation model of the studied
system. In Colledani and T.Tolio [2006] authors applied the decomposition method to
develop performance evaluation model for manufacturing systems monitored by SPC
with online inspection. They have considered both 100 percent inspection and sampling
policies in their model. In Borgh et al. [2007] they have extended the Colledani and
T.Tolio [2006] approach to the analysis of manufacturing systems with online quality
control systems and rework of non-conforming components. In Colledani and T.Tolio
[2009] an approximate analytical method is developed based on system decomposition
for evaluating the manufacturing systems monitored by SPC, including scrape and fi-
nite buffers explicitly.
The decomposition method attracted interests of practitioners in several manufacturing
context as well. For instance, in Patchong et al. [2003] they have developed an analytical
approach based on decomposition method combined with simulation model to analyze
and improve the performance of car body shop of SPA Peugeot Citroen. Alden et al.
[2006] reported an application of analytical approach based on decomposition method
for performance evaluation in several sectors of General Motors. Colledani et al. [2010]
proposed a new methodology, based on analytical methods, to support SCANIA in
manufacturing system productivity improvement through re-configuration. The ana-
lytical approach is based on the decomposition and the application of this approach to
the SCANIA six-cylinder engine-block machining line enabled a remarkable increment
in throughput by selecting analytically the most suitable improvement actions.
2.2.3 Traditional Assembly Systems Performance Measurement
To get insights about the sub-assembly level strategy of the final assemble quality im-
provement, we need to study the performance of traditional assembly systems from the
system point of view. There are wide verity of research conducted in this area.
The first comprehensive survey which is conducted in analysis of performance of assem-
bly system is Gershwin [1991]. He described a single part type assembly-disassembly
18
2.2. REVIEW OF ANALYTICAL MODELS: EXACT METHODS ANDAPPROXIMATE METHODS
Figure 2.2: Assembly System Decomposition Example.
production system as a network with discrete material, unreliable machines, and fi-
nite buffers. In order to evaluate the overall performance of the system in terms of
production rate and average buffer levels, he proposed to decompose the system to
two-machine, one buffer lines which is called building block. The flow of material in
the buffer of each building block approximates the behavior of the original system.
He has developed equations that relates the original line machines’ parameters to the
building block machines’ parameters. In order to solve the decomposition equations,
he applied the Otero-DDX algorithm which is based on Dallery-David-Xie (DDX) al-
gorithm (DALLERY et al. [1988]). Otero-DDX is an algorithm which propose the
evaluation sequence of the building blocks of assembly/dis-assembly models. Figure
2.2 represents an example of the decomposition application in the assembly system
performance evaluation method.
19
2. THEORETICAL BACKGROUND: PERFORMANCEEVALUATION METHODS IN MANUFACTURING SYSTEMS
Mascolo et al. [23(4] focused on the system similar to the Gershwin [1991], while they
have consider the continuous flow of the materials in assembly line. Therefore the
features of the system that they have considered are: homogenous assembly lines, un-
reliable machines with exponential failure and repair times, and finite buffer capacities.
The systems of single part type, homogenous assembly-disassembly production system
with continuous material, exponential failure and repair time distributions unreliable
machines, and finite buffers is considered in Gershwin and M.Burman [2000]. By inho-
mogeneous he means the machines processing times could be different along the line.
The author developed decomposition equations in order to approximate the machines
behavior in decomposed building blocks. He has proposed an algorithm to solve de-
composition equations which follows the DDX algorithm and its extension, the ADDX
algorithm (M.Burman [1995]), however the proposed algorithm reduced the computa-
tional time.
JEONG and KIM [1998] proposes an efficient method to estimate the throughput and
average buffer levels of Assembly/Disassembly systems. They have studied an Assem-
bly/Disassembly system which has the finite buffer capacities, repair time and failure
time are distributed exponentially, and the processing time of machines are different
and they are distributed exponentially as well. They use the decomposition approach
to estimate the performance of the line. Equations to compute the failure, repair and
processing times of each building block is derived based on the interruption of flow, re-
sumption of flow and the flow rate-idle time relations. Different but fixed processioning
time has been studied in Gershwin and M.Burman [2000], but JEONG and KIM [1998]
proposed an algorithm to transfer stochastic processing time to homogenous system in
such a way that the transferred system performs close to the original system.
20
3
Selective Assembly System
Conventions, System Description
and Analytical Performance
Evaluation Methodology
In this thesis we have two sets of conventions for our modeling procedure of selective
assembly systems, the first set is regarding to the assembly process and we call them
Mechanical Assemblies Conventions and the second set of conventions is regarding to
the manufacturing system level assumptions and we call this set System level Conven-
tions.
3.1 Mechanical Assemblies Conventions
1- Key Characteristic Distributions Of The Sub-assemblies.
we assumed that there are models for how the key characteristic of sub-assemblies are
distributed statistically. The partitioning techniques for selective assembly and the
scrapes that we have to impose to sub-assemblies are based on these distributions. In
practice, these data are collected from the history of the manufacturing process there-
fore the actual data are used to generate the statistical distributions, while in cases
that are not available, the nominal process mean value is considered as the distribution
mean and the standard deviation is estimated from the similar characteristics in a simi-
21
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
lar production environment (Whitney [2004]). In addition, the key characteristic values
of sub-assemblies are an independent random variables because the manufacturing er-
ror, which is the variation cause, is composed by several independent error sources.
According to Central Limit Theorem (Miller and Miller [2004]) the key characteristic
(for example the dimension) can follow normal distribution when there is no significant
source of error.
2- No Process Mean Drift.
Commonly, in manufacturing processes due to tool wear out or using a different mate-
rial and so on, there are process mean drift which cause the shift in the mean nominal
value. We assume that in manufacturing process Statistical Process Control is applied
and there are no mean drift.
3- Assembly Task Time and Assembly Error.
We assume sub-assemblies can be placed simply in correct location and orientation
during assembly process. This can be done reliably and repeatably, and does not need
operator skills. Therefore, assembly process is well suited for mass production and
assembly task time is homogeneously with the other manufacturing processes.
4- Single Key Characteristic For The Sub-assemblies.
We assume that through mathematical engineering analysis of sub-assemblies’ key char-
acteristic on the assemble key characteristic (AKC), there is only a single sub-assembly
key characteristic (only dimensional and not geometric) that final assembly quality is
sensitive to. In practice it is suggested to minimize the number of influential key char-
acteristic of sub-assemblies on the quality of final assembly.
5- Rigid Body Sub-assemblies (no deformations).
There are no variation buildup in assembly due to the sub-assemblies stress-strain con-
siderations (Whitney [2004]). For example, in sheet metal parts fabrication, process
contains forming and die machines which cause variations due to spring-back phe-
nomenon. Therefore, to simplify our model we assume that part have no spring-backs
and no stress-strain effects on the assembled part variations.
22
3.1. MECHANICAL ASSEMBLIES CONVENTIONS
6- Measurement Error.
There is no significant measurement error, and by significant we mean sub-assemblies
will not be mixed in terms of quality classes in dedicated buffers due to measurement
error. In addition, considering no measurement error, there are no confirming parts
who are rejected and there are no non-conforming parts accepted both in manufactur-
ing stage and assembly stage.
3.1.1 Manufacturing System Conventions
1- Two Sub-assemblies.
In this thesis we study the assembly system which assembles two components to ob-
tain the final product. In real world, products are consist of several sub-assemblies
and rarely we can find an assemble consist of two components, however assuming two
separate sets of components and considering each set as a single sub-assembly is not
far from reality. Therefore, we assign one key characteristic for each set of components
and we consider it as unique sub-assembly key characteristic.
2- Stations Integration.
Sub-assemblies are made through several operations and naturally there is no single
stage manufacturing process. We assumed all the manufacturing elements are aggre-
gated in a single station for each sub-assembly production (we have two manufacturing
stations according to Manufacturing System Conventions 1) and the same applies for
assembly station. Beside, both the manufacturing machines are fully dedicated to the
assigned sub-assemblies. Therefore, machines capacity are all equal to 1 for each sub-
assembly manufacturing as well as assembly process.
3- Human Resource Interaction.
We assumed human resource are available and reliable all the time and there is no dis-
ruptions due to labor resource. Therefore, if production rate increases, although labor
relations may suffer, but we ignore the effect to simplify the system analysis.
4- No System Learning.
When essential system disruption happens in manufacturing system, managers usually
23
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
try to find the source of disruption and they prevent that disruption to happen again.
However, we assume that we respond to disruption by introducing buffers to the system
so that the disruption can be mitigated. Therefore, when any machine fails its adja-
cent machine may continue the operation. Therefore, in this thesis we ignore system
learning because we prefer to study the performance of the fixed system first, then
uncertainty of parameters (for example uncertainty of failure and repair parameters)
could be studied in future complementary studies.
3.2 Selective Assembly System Description
A typical system of the proposed class is represented in Figure 3.1. Although this sys-
tem can be extended into a wider process-chain, including upstream component man-
ufacturing processes and downstream manufacturing processes for further processing
of the assembled component, in this thesis we will specifically focus on the integrated
quality and production logistics performance of the selective assembly cell. Specifically,
we consider a selective assembly system where two sub-assemblies, namely X and Y,
are assembled. Extensions to higher number of sub-assemblies are possible, within the
same framework.
As shown in Figure 3.1 the sub-assemblies X and Y are respectively processed by ma-
chines Mx and My (blue squares). After the manufacturing process, each sub-assembly
is inspected (red squares) and placed into the dedicated buffers (yellow circle), accord-
ing to the measured key quality characteristic value.
For sub-assembly X (or Y ) the dedicated buffers are denoted as Bix(or Bi
y ) with
i=1,...,F. Buffers have finite capacity N ix and N i
y , with i=1,...,F. A sub-assembly X
is assembled with one sub-assembly Y of the same class by the assembly station Ma
(light blue rectangle).
The detailed characteristics of the manufacturing machines and inspection stations
and the characteristics of the assembly machine are discussed in the following, with
particular emphasis on the policies regulating their part flow control mechanisms.
24
3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION
Figure 3.1: Selective Assembly System Topology
3.2.1 Manufacturing machines and inspection stations
In the described system, both Mx and My are manufacturing machines dedicated to
the sub-assembly X and Y manufacturing process, respectively. However, since they
share the same system behavior, we will focus on the description of Mx. Without loss
of generality, the same notation is applied for the sub-assemblies manufactured in My
with proper modification of sub/superscription.
As illustrated in Figure 3.2, Mx is an integrated machine formed by two stages in se-
ries. The first stage is the machining station which processes the key feature of the
component; the second stage is an inspection station dedicated to the on-line measure-
ment of the processed quality feature. After inspection and based on the sub-assembly
quality feature measurement, the processed sub-assembly is deposited in one of the
downstream buffers. For regulating this process, a partitioning policy is defined so that
the measured sub-assemblies are characterized by their quality class. Each quality class
is connected to the specific buffer, therefore, manufactured sub-assemblies are deposited
in dedicated buffers based on key quality characteristics.
The machine Mx is unreliable and it fails while producing a sub-assembly x with prob-
ability Px = 1/MTTFx and it is repaired with probability rx = 1/MTTRx. Time
to failures are assumed to be geometrically distributed. From a material flow point
25
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.2: Machine X system topology.
of view, the sub-assembly manufacturing and inspection station Mx acts as a splitting
stage, that sorts the incoming material flow into F output flows. However, the splitting
fractions are not fixed and known a priory but they depend on the sub-assembly key
characteristic distribution.
Component quality. Stage Mx produces parts with key quality characteristic values
distributed according to a known probability density function fx (As mentioned in
conventions, the statistical distribution of the sub-assemblies key characteristic is known
and fix). The mean of the distribution is µx and the standard deviation is σx. On this
feature, Specification Limits are imposed by design process. They are defined as Upper
Specification Limit (USLx) and Lower Specification Limit (LSLx). According to these
limits, a component can be defective if its quality characteristic is out of the defined
limits. Defective components x are identified and scrapped by the inspection station
located downstream of manufacturing machine Mx. The manufacturing processes of
sub-assemblies X and Y may have different capabilities.
Partitioning Policy. When a sub-assembly is manufactured, its key quality feature
is measured and it is partitioned into a specific quality class according to the mea-
sured value. For sub-assembly X, Cx quality classes are defined. Each class contains
sub-assemblies with key quality feature values included between two limiting values.
Therefore, for each quality class cx, the lower limit lXcx and the upper limit LXcxof the
quality feature belonging to that class are defined. The quality classes are contiguous,
i.e they respect the following properties:
26
3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION
LXcx = lXcx+1 ∀cX = 1, ..., Cx − 1 (3.1)
LCx = USLX
l1 = LSLX
In the case of equal width partitioning scheme for partitioning,
LXcx − lXcx =
USLX − LSLXCX
∀cX = 1, ..., CX (3.2)
In general definitions, the number of quality classes generated for sub-assemblies x
and y is the same, i.e. CX = CY . Equation 3.3 defines the sorting policy, αXcx is the
probability of sorting a part after inspection into quality class cx:
αXcx =
∫ LXcx
lXcx
Fx(s)ds (3.3)
Each quality class cx is connected to the specific buffer BXi , with i = 1, ..., F . It means
there is a one-to-one association between buffers and quality classes.
3.2.2 The Assembly Machine
The assembly station Ma assembles one sub-assembly X with one sub-assembly Y to
meet a desired key quality characteristic value of the assembled product, shown in
Figure 3.3. From a material flow point of view, the assembly station Ma acts as a
merging stage, that merges the F incoming material flows into a unique output flow
while each flow has an assembly operation. Stage MA is unreliable and it fails while
producing a part with probability Pa = 1/MTTFa and it is repaired with probability
ra = 1/MTTRa. Times to failures and time to repairs are assumed to be geometrically
distributed.
Assembled product quality. We denote z as the key quality characteristics of the
assembled product which is expressed in form of a function z = g(x, y) of the sub-
assemblies’ key quality feature values x and y. Therefore, the probability density func-
tion fz and the cumulative distribution function Fz can be obtained by the cumulative
27
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.3: Assembly Machine System Topology.
distribution functions of x and y. Specification Limits are imposed by design on the
assembly key characteristic z. They are defined as Upper Specification Limit (USLz)
and Lower Specification Limit (LSLz). If the value of z exceeds these limits, the as-
sembled product is non-conforming. According to this tolerance, every assembly flow
has a specific fraction of non-conforming parts associated, namely γai , with i = 1, .., F .
For example, consider the aforementioned application of the remote laser welding pro-
cess in the automotive industry. In this case, the gap between the key quality feature of
sub-assemblies X and Y is the key quality feature z of the assembled product. In more
details, the key quality characteristic of the final assembly is the weld stitch quality
that strictly depends on the gap between the two metallic plates to be welded. The
gap (z) is measured and controlled and have to be | x− y | to generate the proper weld
stitch. In case of z = g(x, y) ≤ 0.1 the gap is too tight and the vaporized zinc has no
space to flow out of the welded metals and cause porosity in the welds stitches. On the
other hand, if z = g(x, y) = |x− y| ≥ 0.3 the gap is too high and the two metals cannot
be joint properly due to lack of fusion. In both cases the final assembly is identified as
non-conforming part (Steen [1993]).
If a unique quality class is present for components X and Y , i.e. selective assembly
is not adopted, the fraction of defective assembled products can be directly estimated
28
3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION
from the cumulative function Fz and the specification limits imposed on z. However, in
selective assembly the assembled products are generated by matching specific quality
classes, cx and cy, of the sub-assemblies. Therefore, for each possible combination of
quality classes of X and Y , cx and cy, the normalized cumulative function FZcx,cy has
to be computed, for example by convolution. Then, the fraction of generated defective
products γ (cx, cy) for each matched class be calculated as:
γ(cx, cy) = 1− F zcx,cy(USLz) + F zcx,cy(LSLz) (3.4)
Matching Policy. A matching policy couples a buffer of sub-assemblies X with one
compliant buffer of sub-assemblies Y . In this thesis, a one to one matching between
buffers of component X and Y is assumed. In other words, the assembly machine Ma
can assemble components X in buffer Bxi only with sub-assemblies Y in buffer By
i , with
i = 1, ..., F . Therefore, F possible output flows are generated, obtained by joining the
sub-assemblies in the F existing buffers.
Assembly Policy. The assembly machine selects the compliant buffers according to
a probabilistic rule, similar to the part type selection rule proposed in (Colledani et al.
[2005]). If all the upstream buffers are not empty, which is all the coupled buffers are
available to be selected, than the assembly machine selects buffer i with fixed proba-
bility αai , with∑F
i=1 αai = 1. If one or more upstream buffer is empty, the selection
probability is scaled according to the available components. If all the upstream buffers
are empty, the machine is starved.
It must be noticed that although both the assembly policy and the partitioning policy
(after the manufacturing processes) are probabilistic, there is a fundamental difference
between these policies. In the assembly policy there is always full control of the pro-
cess, in the sense that the assembly machine has the intelligence to decide which flow
is better to process. On the contrary, in the partitioning policy the quality class of a
given sub-assembly cannot be imposed a priory, but it is a result of measuring the key
quality characteristic which is a consequence of the process variation.
The smart property of the assembly machine for selection of the the proper flow, per-
mitted us to introduce new flow control policies to improve the material flow of selective
29
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
assembly systems. These policies show great improvement in the system performance
of selective assembly systems. We explained the policies in details and their effect in
the next chapter.
3.2.3 Modeling Assumptions and Notations
A list of modeling assumption that we have used in this thesis is described in the
following.
• The dynamics of the material flow is modeled as a discrete flow of parts. All
operational machines start their operations at he same instant. Therefore the
time is considered as discrete. Moreover, the states of the system are discrete.
• Each machine has the fixed and same processing time which is known in advanced.
The processing time is scaled to the time unit (synchronous manufacturing sys-
tem).
• Operational dependent failures: machine could fail only while processing a part.
Therefore, when the machine is blocked or starved (which is idle in general),
cannot fail.
• Each machine is unreliable and subject to multiple failure modes. Machine failures
are uncorrelated, i.e., they are independent of the state of the rest of the system.
• If operational, a machine starts processing one part at the beginning of the time
unit. The buffer levels are updated at the end of the time unit.
• The manufacturing machines are never starved, i.e., there is an infinite number
of sub-assemblies waiting to be manufactured upstream the Mx and My.
• The assembly machine is never blocked, i.e., there is enough space for sub-
assemblies to be deposited in downstream of MA.
• Blocking before service (BBS ): If the downstream buffer is full, the machine is
prevented from doing any operation.
• An operational machine can fail in only one of its failure modes.
30
3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION
• When a machine breaks down, the part it was processing on is returned to the
upstream buffer to wait for the machine to get repaired and process can resume.
• Inspection and transportation are assumed to take negligible time comparing to
the operations time.
3.2.4 Deadlock States
Observing the dynamic of system behavior, a deadlock state is observed due to the
system logistic complexity and finite buffer capacity. If all the following conditions
hold in the system, the associated state is called deadlock state:
1. Machine Mx cannot deposit sub-assembly X of quality class i in buffer Bxi since
it is full;
2. Machine My cannot deposit sub-assembly Y of quality class j in buffer Byj since
it is full;
3. The assembly machine MA cannot assemble parts from any couple of upstream
buffers because there are no complaint sub-assemblies to be assembled.
Figure 3.4 and Figure 3.5 describe better the deadlock states for the selective assembly
system with two quality classes. In the case of two quality classes, there are two separate
deadlock state that the system might visit. The black circles illustrate the full buffer
while the white circle shows the empty buffer. Observing Figure 3.4, the manufacturing
machine Mx and My are blocked because one of the downstream adjacent buffers are
full. They cannot start process because the processed sub-assembly might belong to
the full buffer class after measurement and following the Blocking Before Service (BBS)
rule the machine must be blocked. The assembly machine is starved because one of the
matched buffers contain no sub-assemblies for process, one sub-assembly buffer is full
while the other is empty. Figure 3.5 illustrates the same behavior of the system while
the full buffers are the opposite of the Figure 3.4.
31
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.4: Deadlock state 1 for the Selective Assembly with two quality classes.
Figure 3.5: Deadlock state 2 for the Selective Assembly with two quality classes.
32
3.2. SELECTIVE ASSEMBLY SYSTEM DESCRIPTION
To characterize more formally the deadlock state, considering the buffer levels described
by the vector n = (nx1 , nx2 , ..., n
xF , n
y1, n
y2, ..., n
yF ), a deadlock state is every state under-
going the following condition:
(nxi = Nxi ∧ n
yi = 0) or (nxi = 0 ∧ nyi = Ny
i ) ∀i = 1, ..., F (3.5)
Notice that we are required to design a selective assembly system which avoids visiting
the deadlock state. In deadlock state, the assembly machine is starved since there are
no upstream non-empty coupled buffers as the same time the manufacturing machines
(Mx and My) are blocked because one of their downstream buffers is full. Consequently,
the system is completely absorbed in deadlock state.
Deadlock avoidance policies. To avoid the deadlock state the following policies
have been introduced for these systems. According to (Thesen and Jantayavichit [1999])
two strategies are possible:
• Discard: discard incoming sub-assemblies that cannot be accommodated in the
selected full buffer.
• Ignore: allocate sufficient space to accommodate all space demand.
The discard policy is characterized by a strict partitioning policy is always followed,
i.e. each quality class is always dedicated to a unique buffer. Thus, whenever a sub-
assembly is produced, either at machine Mx or MY , that cannot be deposited in the
downstream buffer where this sub-assembly is sorted since this buffer is full, the sub-
assembly is discard and a new sub-assembly has to be processed by the machine. It
can be proved that under this policy the deadlock condition is never reached.
Although this policy entails a loss of throughput, it preserves the assembly yield (frac-
tion of conforming assembled parts). This is because the assembly machine remains
with the selection of sub-assemblies based on the pre-defined quality classes.
33
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
The total throughput, which is total production rate including the non-conforming
parts, is reduced due to the fact that the manufacturing stages are processing sub-
assemblies and when the station is blocked by a single buffer, they discard the pro-
cessed sub-assembly belonging to the corresponding full buffer. By doing this, there
are fraction of conforming sub-assemblies totally neglected for assembly process.
In real life manufacturing, discarding the sub-assemblies is mostly placing the compo-
nents out of the classification system, while sub-assemblies has its quality attribute and
there is possibility to be assembled.
The Ignore policy introduce a very high level of work in progress to the system in order
to avid the deadlock state which implicitly ignores the limited buffer sizes. Therefore,
in order to develop our analytical performance evaluation method, we considered the
discard policy to proceed.
3.3 System Performance Measures
To analyze the performance and system behavior of selective assembly systems the
main system performance measures of interest are:
• Average total production rate of the system, THTot:
the final assembled production rate [parts/time unit] delivered in output by the
system, considering both conforming and non-conforming assemblies. Starting
from the total production rate of every assembled flow i = 1, ..., F , it can be
derived as:
THTot =F∑i=1
THToti (3.6)
• Average effective production rate, THEff :
the final assembled production rate [parts/time unit] delivered in output by the
34
3.4. TWO-LEVEL DECOMPOSITION APPROACH
system, considering only conforming assemblies. It can be obtained as:
THEff =
F∑i=1
THToti Yi (3.7)
• System yield, Y system:
the fraction of conforming assemblies delivered in output by the system. It can
be obtained as the rate between the effective and the total throughput:
Y system =EEff
ETot(3.8)
• Average level of buffers, n̄xi and n̄yi :
the average amount of parts accumulated in each buffer.
• Average total Work in Progress, WIP:
the average number of parts flowing in the system.
WIP =n∑i=1
n̄xi +n∑i=1
n̄yi (3.9)
3.4 Two-level Decomposition Approach
In order to evaluate the performance of a selective assembly systems, an extension of
the decomposition technique proposed in Colledani et al. [2005] is used. The general
idea of the approach is the following: for each buffer in the original line, a building
block is dedicated that is formed by two pseudo-machines and one buffer, as represented
in the right side of Figure 3.6. Each building block is analyzed by using the method
in Tolio et al. [2002], and the results are propagated among sub-systems by using the
35
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.6: Two level decomposition approach for selective assembly systems.
so-called DDX algorithm proposed in DALLERY et al. [1988].
Since in the described selective assembly system the sub-assembly manufacturing ma-
chines act as split machines and the assembly machine acts as a merge station, their
behavior cannot be matched by simple multiple failure mode models. Indeed, more
than one input or output flows are available and this generates additional complexity
in the machine behavior. Therefore, they cannot be directly considered in the decom-
position. In other words, there is a gap between the structures of the Markov chains
modeling the behavior of the machines in our system and the structures of the Markov
chains accepted by available decomposition methods. Thus, a preliminary analysis of
these complex machines is needed. In fact, the proposed method to develop analytical
performance evaluation method differs from the classical decomposition. In Colledani
et al. [2005] a similar approach was applied to flexible machine processing multiple
part-types and the method was named Two-level Decomposition (Figure3.6).
The first level of analysis is based on the evaluation of all the state probabilities of each
station (two manufacturing machines, Mx and My and the assembly machine). These
36
3.4. TWO-LEVEL DECOMPOSITION APPROACH
probabilities are obtained by solving discrete time-discrete state Markov chains repre-
senting the behavior of such complex machines, also taking into account the influence
of their adjacent buffers. Considering the selective assembly system topology, there are
three Markov chains which represent the states of whole the system. In each Markov
chain, some of transition probabilities are not known. For example for Markov chain
representing the Mx there are probabilities of blocking which is unknown, similarly, for
Markov chain of Ma there are starvation probabilities which are unknown. However,
the starvation and blocking probabilities can be derived by studying the probabilities
of upstream buffers being empty and probabilities of downstream buffers being full,
respectively. This level of analysis is named Machine Level Decomposition (MLD) be-
cause the focus of analysis is on the machines states. This preliminary analysis allows
to approximately simplify the behavior of such complex machines with that of multiple
failure modes machines. With these machine models, it is possible to perform the clas-
sical multiple failure mode two-machine line analysis,(Tolio et al. [2002]) which is based
on the exact analytical solution of building block formed by two pseudo-machines and
one buffer.
This second level of analysis is focused on the flow of material crossing the buffer.
Indeed, we assign failure and repair parameters to the pseudo-machines of each build-
ing block in order to mimic the flow of material through the corresponding buffer of
the original line. Therefore, we name this level of analysis Buffer Level Decomposition
(BLD). The unknown parameters for each Markov chains, which is discussed above,
can be obtained from the results of each building blocks.
The order in which the MLD and the BLD are applied to the machines and buffers
in the line is controlled by an algorithm, similar to the DDX DALLERY et al. [1988].
By studying alternately the BLD and the MLD and by using the results obtained in
one level as input for the other level, it is possible to evaluate the performance of the
original complex system, once convergence conditions are met.
The Two-Level Decomposition approach is useful in those cases in which machines with
a complex behavior are included in the system. In this section, we present the analysis
performed in both levels and propose the equations for exchanging the parameters from
37
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
the MLD to the BLD and vice versa. The proposed method is explained in details for
the case of a selective assembly system with two sub-assemblies and two quality classes
F=2, i.e two buffers for each sub-assembly. The analysis and the proposed approach
are similar for the other system topologies in which more than two quality classes are
present for each sub-assembly.
3.4.1 Buffer Level Decomposition
The building block lx(i) is composed of two pseudo-machines Mu,x(i) and Md,x(i)
and the buffer Bx(i). The flow of material through the buffer Bx(i) of the building
block must approximate the flow of material through the corresponding buffer Bxi of the
original system. In order to achieve this goal, failure modes must be assigned to Mu,x(i)
and Md,x(i), relating them to each possible cause for interruption of the material flow
respectively entering and leaving the buffer.
3.4.1.1 Upstream Pseudo-machine
Considering the flow of material entering the original buffer Bx(i), it can be interrupted
for different reasons. For each possible cause of interruption of the material flow entering
the buffer Bx(i), a failure mode is assigned to the upstream pseudo-machine Mu,x(i).
In general for machines with split property there are two kinds of failure modes which
are assigned to the machine. The Modified Local Failure and the Competition Failure,
which are described in details in the following.
Modified local failure. The machine Mx in the original line may fail while pro-
cessing a sub-assembly. If the machine of the original system Mx fails, all the pseudo-
machines representing that machine in the building blocks must fail. For this reason,
local failure modes are assigned to Mu,x(i). It must be noticed that, for splitting ma-
chines, the probability of failure in local mode is not the same as the one of the original
machine Mx. It must be increased, considering the probability that the original ma-
chine fails while processing a sub-assembly which will be placed in the other buffer.
Therefore, the probabilities of local failures must be adjusted to take into account this
situation. The failure probabilities pu,xt (i) are therefore unknown and will be provided
in output by the MLD. The repair probabilities ru,xt (i) are instead the same as the
38
3.4. TWO-LEVEL DECOMPOSITION APPROACH
repair probabilities of the original machine Mx, i.e. ru,xt (i) = rxt , for each i = 1, 2 and
t = 1, .., Tx.
Competition failure. When a machine of the original system is operational (in
the UP state) but it is processing the sub-assemblies that will not be placed in the
buffer Bx(i) belonging to considered building block, the corresponding pseudo-machine
Mu,x(i) sees an interruption of flow (while the machine is actually operational) and is
considered to be failed. In the other words, although the machine is operational and
working, the processed sub-assembly will not be accommodated in the observed buffer.
This failure mode of the pseudo-machines was introduced for studying multiple part
type systems (Colledani et al. [2005]). The failure and repair probabilities pu,xTx+1(i) and
ru,xTx+1(i) are unknown and will be provided in output by the MLD.
3.4.1.2 Downstream Pseudo-machine
Considering the flow of material leaving the original buffer Bx(i), it can be interrupted
for different reasons. For each possible cause of interruption of the material flow leaving
the buffer Bx(i), a failure mode is assigned to the pseudo-machine Md,x(i). There
are three kind of material interruption flow which are considered as failure modes for
downstream pseudo machine, Modified Local Failure and Competition Failure which
are similar to upstream pseudo machine and the third mode is Remote Failure. In the
following each of these are described in details.
Modified local failure. The assembly machine MA in the original line may fail while
assembling the two sub-assemblies. If the machine of the original system MA fails,
all the pseudo-machines representing that machine must fail. For this reason, local
failure modes are assigned to Md,x(i). It must be noticed that, for a merging machine
performing assembly, the probability of failure in local mode is not the same as the
one of the original machine MA. It must be increased, considering the probability that
the original machine fails while assembling sub-assemblies taken from another couple
of matching buffers. The failure probabilities pd,xt (i) are therefore unknown and will be
provided in output by the MLD. The repair probabilities rd,xt (i) are instead the same
as the repair probabilities of the corresponding original machine MA, i.e. rd,xt (i) = ra
for each i = 1, 2 and t = 1, .., Tx.
39
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Competition failure. When the assembly machine MA is operational but it is as-
sembling matching sub-assembly taken from a flow different from the considered buffer
Bx(i), the corresponding pseudo-machine Md,x(i) is considered failed (while the as-
sembly machine is operational). As mentioned earlier this failure mode of the pseudo-
machines is named Competition Failure. The failure and repair probabilities pd,xTx+1(i)
and rd,xTx+1(i) are unknown and will be provided in output by the MLD.
Remote failure. When the buffer Bx(i) is not empty but the machine Ma can-
not assemble parts from the considered flow i because the matching sub-assemblies
Y stored in the buffer By(i) are not available (i.e. By(i) is empty) the correspond-
ing pseudo-machine Md,x(i) is considered as failed machine. This failure mode of the
pseudo-machines is named Remote Failure, since the cause for the interruption of flow
comes from a different machine in the system. The failure probabilities pd,xTa+1+j(i) with
j = 1, .., Ty, are unknown and will be provided in output by the BLD. The repair
probabilities rd,xTa+1+j(i), with j = 1, .., Ty, are instead the same as the repair proba-
bilities of the pseudo-machine Mu,x(i), which is responsible for causing the starvation,
rd,xTa+1+j(i) = ru,yj (i), for each i = 1, 2 and j = 1, .., Ty.
3.4.1.3 Building Block Analysis
The analysis of the Building Block lx(i) can be performed by using the exact method
proposed in Tolio et al. [2002]. In particular, the average throughput THx(i) and the
average buffer levels, nx(i). Moreover, The blocking probabilities of Mu,x(i) are Pbxk(i),
k = 1, .., Ta + 1 + Ty which is a vector composed by blocking probabilities due to local
failures of assembly machine, competition failure of assembly machine and the local fail-
ure of the machine producing the sub-assembly Y. Similarly, the probabilities of Md,x(i)
being starved, Psxj (i), j = 1, .., Tx + 1, which is a vector of starvation probabilities due
to local failures of the machine processing sub-assembly X are calculated.
40
3.4. TWO-LEVEL DECOMPOSITION APPROACH
3.4.1.4 Inputs to the MLD
The BLD provides input information to the MLD analysis. In particular, the transitions
to blocking states for the MLD analysis of Mx are calculated as follows:
px,b,ik =Pbxk(i)
Ex(i)rx,b,ik i = 1, 2; k = 1, ..., Ta + 1 + Ty (3.10)
rx,b,ik (i) = rd,xk (i) i = 1, 2; k = 1, ..., Ta + 1 + Ty
Similarly, the transitions to starvation states for the MLD analysis of Ma are derived:
px,s,ij =Psxj (i)
Ex(i)rx,s,jj i = 1, 2; j = 1, ..., Tx + 1 (3.11)
rx,s,jj (i) = ru,xj (i) i = 1, 2; j = 1, ..., Tx + 1
The summary of the buffer level decomposition for building block lx(1) and the param-
eters which will be transferred to the machine level decomposition (MLD) is depicted
in Figure 3.7.
3.4.2 Machine Level Decomposition
In the buffer level decomposition analysis that we have explained above, there are input
and output parameters that we transfer to MLD. In this section we describe in details
the MLD analysis and the data transfer for each machine separately.
3.4.2.1 Sub-assembly Manufacturing Machines: Mx and My
State Transition Diagram. The Markov chain representing the behavior of the
sub-assembly manufacturing machine Mx is represented in Figure 3.8 (to simplify the
picture, transition probability p̄ is shown instead of 1 − p; moreover P1 =∑Tx
t=1 pxt +∑Ta+1+Ty
k=1 px,b,1k ).
The Markov chain of original machine is characterized by all the possible states that
the machine may observe. For example for each local failure mode a unique state is
41
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.7: Buffer Level Decomposition for lx(1).
42
3.4. TWO-LEVEL DECOMPOSITION APPROACH
Figure 3.8: Markov model representing Mx characteristics.
associated. However, in order to simplify the picture, in Figure 3.8 the Markov chain
of Mx is illustrating the macro states of the original machine. This means, all the
state of the same type are grouped into a unique aggregated state, without considering
the different failure mode. Each aggregated state is defined by two state indicators,
the first term refers to the first downstream buffer (Bx1 ) and the second refers to the
second downstream buffer (Bx2 ). Each state indicator can assume three different states,
Blocked (B), Working (W), and Down (R).
The aggregated states probabilities in steady state are obtained by adding up all the
43
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.9: State transition diagram for upstream Pseudo machine L(x1).
probabilities of the states of the same type. For example the probability of the aggre-
gated state (RB2) which indicates the state in which the machine is locally down while
the Bx2 is full, is obtained by adding up all the probabilities of the (RiB
2) states over
the local failure modes of the machine (π(· · · ) is indicating the steady-state probability
of the state in brackets)., i.e.,
π(RB2) =
Tx∑i=1
π(RiB2) (3.12)
It must be notice that while we have shown the aggregated states in the Markov chain
(Figure 3.8), in the writing the equations we have distinguished all the states based on
the failure modes to correctly valuate the Markov chain state probabilities. Obviously,
the machine Mx cannot be in both working and down state at the same time, thus the
states (R1W 2) and (W 1R2) are not feasible and not represented in the state transi-
tion diagram. Also the aggregated state (R1R2) represent the state in which both the
downstream buffers are not full and the machine is locally failed. This state is shown
as (R).
In the following we describe some characteristics of the Markov model representing the
Mx behavior,
• If the machine is working and both downstream buffers are not full, the state is
shown as (W 1W 2). Since machine is subject to local failures, from state (W 1W 2)
it may go into state (R) which is the down state. If one of the buffers become full
44
3.4. TWO-LEVEL DECOMPOSITION APPROACH
and the machine is still operating, machine state is shown as (W 1B2) or (B1W 2)
depending on the the full buffer.
• When the machine is in state (W 1B2) and the machine is operating, it may process
a sub-assembly which belongs to the second quality class after measurement. Due
to the fact that the second quality class is connected to the full buffer, the sub-
assembly is discarded based on the Discard rule for deadlock avoidance policy.
The probability of the discard in this state is π(W 1B2)αx2 . The same might
occur for the the state (B1W 2) when the machine processes a sub-assembly that
will be belong to the first quality class, the discard probability is obtained by
π(B1W 2)αx1 .
• When the machine is in the state (W 1B2) or (B1W 2), it mail locally fail and the
corresponding Markov chain goes to state (RB2) or (B1R).
• If the machine is in operating state and the two downstream buffers are both full,
the state is indicated as (B1B2). If the assembly machine selects the sub-assembly
from Bx1 , the Markov chain representing machine Mx goes to state (W 1B2) and
if the assembly machine selects the sub-assembly form Bx2 the Markov chain goes
to state (B1W 2).
Therefore, depending on the level of the adjacent buffers, machine Mx behaves, as re-
ported in summary in Table 3.1. As it can be noticed, the discard policy affects the
behavior of the machine in the states where one of the two buffer is full and the other
is not full (row 1 to row 4). The probability of failure and repair of machine Mx, i.e. px
and rx, are known since they are input data of the problem. It must be noticed that,
in the Markov chain of original machine Mx (similarly My), the competition failure is
not considered because this machine is able to produce for both quality classes, which
means for both buffers. In the other words, the Markov chain characterizes the original
machine and two adjacent downstream buffers, thus observes the states concerning two
possible quality classes.
As it can be noticed from the Markov chain, the probabilities of transition to blocking
states are unknown and cannot be derived directly from the original system. However,
through the appropriate equations in BLD (see equation 3.10: the unknown parameters
45
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Buffers Part qualityMachine State
Discard Rule
Bx1 Bx
2 Class Output Buffer Prob.
Not Full Full 1 UP(W 1B2) Bx1 αx1
Not Full Full 2 UP(W 1B2) discard αx2
Full Not Full 1 UP(B1W 2) discard αx1
Full Not Full 2 UP(B1W 2) Bx2 αx2
Not Full Not Full 1 UP(W 1W 2) Bx1 αx1
Not Full Not Full 2 UP(W 1W 2) Bx2 αx2
Full Full 1-2 BL(B1B2) / /
Not Full Full 1-2 DOWN(RB2) / /
Full Not Full 1-2 DOWN(B1R) / /
Not Full Not Full 1-2 DOWN(R) / /
Table 3.1: behavior of machine Mx. ”B” denotes blocking states, ”W” denotes opera-
tional states, and ”R” denotes down states.
of the MLD are function of the output parameters of the BLD. ) they can be obtained.
Therefore, all the transition probabilities in this Markov chain are known and the
unique stationary distribution can be calculated.
Machine Level Analysis. By analyzing the Markov chain in Figure 3.8, the steady-
state probabilities of Mx can be derived (as mentioned earlier, the same procedure is
applied to obtain the steady state probabilities of the Markov chain characterizing the
machine My). Then, the upstream pseudo-machines Mu,x(i), i = 1, 2 is characterized
by approximating the Markov model of Mx steady states. The Markov chain in Figure
3.8 can be solved and the steady-state probabilities can be calculated. Then, in order
to match the simplified multiple failure mode machine structure, the Markov chain of
Figure 3.8 is transformed into the Markov chain of Figure 3.9. The transformation
is made through the re-distribution of the calculated steady-state probabilities, per-
formed by using the following State Aggregation Equations. For Mu,x(1), the following
equations are adopted (3.13 3.14 3.15 3.16):
π (W u,x(1)) = π(W 1W 2
)αx1 + π
(W 1B2
)αx1 (3.13)
46
3.4. TWO-LEVEL DECOMPOSITION APPROACH
where π (W u,x(1)) indicates the state in which the Pseudo machine Mu,x(1) is operating
(the original machine is processing sub-assemblies for the buffer Bx1 ). In order to obtain
this state, we need to sum up the portion of the state (W 1W 2) and (W 1B2) that the
machine is processing for Bx1 . It must be notice that in the state (W 1B2) due to the
lack of control on the flow of material, there are some portion of the sub-assemblies
directed to Bx1 , which are discarded consequently. We must consider only αx1 percent
of the state as operational state for Mu,x(1).
π(W̄ u,x(1)
)= π
(W 1W 2
)αx2 + π
(W 1B2
)αx2 (3.14)
The state π(W̄ u,x(1)
)is considered as a failure mode for Mu,x(1), because the original
machine is processing the sub-assemblies for Bx2 . This state can be obtained by adding
up the proportion of the (W 1W 2) state in which the sub-assemblies belong to Bx2
((W 1W 2)αx2) and the proportion of the (W 1B2) state in which the sub-assemblies are
discarded.
π (Bu,x(1)) = π(B1W 2
)+ π
(B1B2
)+ π(B1R2) (3.15)
The blocking state of the Mu,x(1) is the states of the original machine in which the
machine is idle from Mu,x(1) point of view. The (B1W 2) state is completely involved
because even if the original machine processes the sub-assembly for Bx1 , still the sub-
assembly is discarded. The second term of the right hand side, (B1B2), is the state in
which the original machine is idle because both buffers are full, thus from Mu,x(1) point
of view the Pseudo machine is idle as well. The third term, (B1R2) is added because
the original machine is idle from the Mu,x(1) point of view due to the observing full
buffer (Bx1 ).
π (Ru,x(1)) = π(R1B2
)+ π (R) (3.16)
The remaining two state of the Markov chain characterizing the machine Mx represent
the state in which machine is locally failed and they sum up to obtain the down state
of the Mu,x(1).
47
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
In order to obtain the state probabilities of the Pseudo Mu,x(2), we need to aggregate
the Markovian state of the original machine in a following manner:
π (W u,x(2)) = π(W 1W 2
)αx2 + π
(B1W 2
)αx2 (3.17)
π(W̄ u,x(2)
)= π
(W 1W 2
)αx1 + π
(B1W 2
)αx1 (3.18)
π (Bu,x(2)) = π(W 1B2
)+ π
(B1B2
)+ π(R1B2) (3.19)
π (Ru,x(2)) = π(B1R2
)+ π (R) (3.20)
Inputs to the BLD. Considering the state transition diagram for the pseudo-machine
Mu,x(1) (Figure 3.9), and knowing all the state probabilities, it is possible to obtain
the modified local failures and the competition failure of the Mu,x(1) (the same for the
modified local failure and the competition failure of Mu,x(2)). As mentioned earlier, it
must be noticed that the probability of local failure for the upstream Pseudo machine
is higher than the local failure probability of the original machine. This is because the
machine might fail while processing the sub-assembly which goes to the buffer of the
other quality class, Bx2 .
We can evaluate the local modified failure parameters of the upstream Pseudo machine
by applying the balancing equation on node (Ru,xt (1)) of state transition diagram of
Figure 3.9. Therefore, the probability of Mu,x(1) failing in local mode can be obtained
as:
pu,xt (1) =π (Ru,xt (1))
π (W u,x(1))ru,xt (1) t = 1, .., Tx (3.21)
48
3.4. TWO-LEVEL DECOMPOSITION APPROACH
and similarly for Mu,x(2) is given as:
pu,xt (2) =π (Ru,xt (2))
π (W u,x(2))ru,xt (2) t = 1, .., Tx (3.22)
In order to obtain the competition failure parameters of Mu,x(1), we apply the balance
equations on the node W̄ u,x(1), due to the fact that we obtained the probability of
W̄ u,x(1) (that represents the state in which the Pseudo machine Mu,x(1) is not pro-
cessing the sub-assembly because the other Pseudo machine Mu,x(2) is processing a
sub-assembly). Thus, the probabilities of failure and repair for the competition failure
mode of the Mu,x(1) can be derived as follows:
pu,xTx+1(1) =π(W̄ u,x(1)
)π (W u,x(1))
ru,xTx+1(1) (3.23)
ru,xTx+1(1) = αx2(1−Tx∑t=1
pxt )
Similarly for the Mu,x(2), we obtain the following equations for competition repair
and failure parameters:
pu,xTx+1(2) =π(W̄ u,x(2)
)π (W u,x(2))
ru,xTx+1(2) (3.24)
ru,xTx+1(2) = αx2(1−Tx∑t=1
pxt )
3.4.2.2 Assembly Machine
The application of the MLD to the assembly machine Ma is presented in this section.
49
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Buffers
Matching flowMachine State Input Buffer Prob.
Bx1 /By
1 Bx2 /By
2
NE E 1 UP(W 1S2) Bx1 /By
1 1
E NE 2 UP(S1W 2) Bx2 /By
2 1
NE NE 1 UP(W 1W 2) Bx1 /By
1 αa1
NE NE 2 UP(W 1W 2) Bx2 /By
2 αa2
E E 1-2 ST(S1S2) / /
NE E 1-2 DOWN(R1S2) / /
E NE 1-2 DOWN(S1R2) / /
NE NE 1-2 DOWN(R) / /
Table 3.2: Behavior of machine Ma. ”S” denotes starvation states, ”W” denotes opera-
tional states, and ”R” denotes down states.
State Transition Diagram. Depending on the level of the upstream buffers, ma-
chine Ma behaves as reported in Table 3.2 (where E indicates that one of the two
buffers is empty, NE indicates that none of the buffers is empty).
The Markov chain of original machine (Ma) is characterized by all the possible states
that the machine may observe. For example for each local failure mode a unique state
is associated. However, in order to simplify the picture, in Figure 3.10 the Markov
chain of Ma is illustrating the macro states of the original machine. This means, all the
state of the same type are grouped into a unique aggregated state, without considering
the different failure mode. Each aggregated state is defined by two state indicators,
the first term refers to the first coupled upstream buffers (Bx1 and By
1 ) and the second
refers to the second coupled upstream buffers (Bx2 and By
2 ). Each state indicator can
assume three different states, Starved (S ), Working (W ), and Down (R).
The aggregated states probabilities in steady state are obtained by adding up all the
probabilities of the states of the same type. For example the probability of the ag-
gregated state (R1S2) which indicates the state in which the machine is locally down
while the second flow of the sub-assemblies are starved, is obtained by adding up all
the probabilities of the (RiS2) states over the local failure modes of the machine, i.e.,
50
3.4. TWO-LEVEL DECOMPOSITION APPROACH
π(R1B2) =
Tx∑i=1
π(RiB2) (3.25)
The assembly machine is starved for one of the flow i if at least one of the two buffers
Bxi or By
i storing the sub-assemblies x and y is empty. The main difference with the
analysis of the split station Mx is the following. If the assembly station is starved since
at least one buffer related to flow f = 2 is empty, then the part is assembled from flow 1
with probability 1. In fact, in the assembly process there is full control of the selection
process. On the contrary, in the sorting process at machine Mx, the quality class of the
next processed part is dependent only on the process variability and cannot be directly
controlled a priory.
The Markov model describing the behavior of the assembly machine is reported in
Figure 3.10. In the following we describe some characteristics of the Markov chain
representing the Ma behavior,
• If the assembly machine is operating and all the upstream buffers are Non-Empty
(NE ), the Markov chain state is (W 1W 2). When assembly machine selects the
coupled upstream buffers the machine state might fall into (W 1S2) or (S1W 2)
depending on the selected coupled buffers and the level of sub-assemblies in the
selected buffers.
• If the assembly machine is in the state (W 1S2) or (S1W 2) and the machine
locally fails Markov model goes to state (R1S2) or (S1R2), respectively. The
Markov model represent the state in which the assembly machine is failed while
one of the couple buffers is starved. If the starvation of the upstream buffer is
resumed while the machine is not repaired, the Markov model transits to (R).
This means the buffers are all Non-Empty while the machine cannot assemble
due to its local failure.
• The system may go to (W 1W 2) from (R1S2) or (S1R2), if the starvation of the
corresponding coupled buffer is resumed and the machine is repaired.
51
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
Figure 3.10: Markov model representing Ma characteristics.
Figure 3.11: State transition diagram for downstream Pseudo machine l(x1).
52
3.4. TWO-LEVEL DECOMPOSITION APPROACH
• If the machine is in state (W 1S2) or (S1W 2) the assembly machine selects the
available coupled buffers (for example Bx2 and By
2 in case the state is (W 1S2)) with
probability of 1. When the selected coupled buffer become starved (obviously the
machine is operating), the system goes to (S1S2).
As it can be noticed from the Markov chain of assembly machine, the probabilities of
transition to starvation states are unknown and cannot be derived directly from the
original system. However, through the appropriate equations in BLD (see equation
3.11) the unknown parameters of the MLD are function of the output parameters of
the BLD. The other parameters of the Markov model of assembly machine is known.
We need to highlight that the transition probabilities which are composed by the local
failures of the assembly machine, the original local failure parameters are used. Be-
cause the modified local failure parameters are applied to interrupt the flow of material
leaving the buffer for building block evaluation. However in the Markov chain model,
the Markov model is characterizing the assembly machine while considering the four
upstream buffers. Also, for the same reason the competition failures are not applied in
the Markov model of the assembly machine.
Machine Level Analysis. By analyzing the Markov chain in Figure 3.10, the steady-
state probabilities of Ma can be derived. In order to characterize the downstream
pseudo-machine structure of each building blocks, Md,x(i), i = 1, ..., 4, the Markov
chain of Figure 3.10 is transformed into the Markov chain of Figure 3.11. The transfor-
mation is made through the re-distribution of the calculated steady-state probabilities,
performed by using the following State Aggregation Equations. For Md,x(1), the fol-
lowing equations (equations 3.26, 3.27, 3.28 and 3.29)are adopted:
π(W d,x(1)
)= π
(W 1W 2
)αa1 + π
(W 1S2
)(3.26)
Where π(W d,x(1)
)denotes the state in which the Pseudo machine Md,x(1) is operating
(the original machine is processing sub-assemblies selected from the coupled buffers Bx1
and By1 ). In order to obtain this state, we need to sum up the portion of the state
53
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
(W 1W 2) in which the assembly machine process the sub-assemblies coupled from Bx1
and By1 , and the total probability of state (W 1S2). It must be notice that in the state
(W 1S2) due to the full control of the flow of material, the assembly machine selects the
first sub-assembly couples and the complete steady state probability is considered.
π(W̄ d,x(1)
)= π
(W 1W 2
)αa2 (3.27)
The π(W̄ d,x(1)
)state is considered as a failure mode for Md,x(1), because the original
assembly machine is processing the sub-assemblies from Bx2 and By
2 while the corre-
sponding coupled buffers are NE. This state can be obtained by considering only the
proportion of the (W 1W 2) state. The assembly machine is able to select the coupled
buffers, in this state the probability of selecting Bx2 and By
2 is αa2.
π(Sd,x(1)
)= π
(S1W 2
)+ π
(S1S2
)+(S1R2
)(3.28)
The starvation state of the Md,x(1) is the states of the assembly machine in which
the machine is idle from Md,x(1) point of view. The (S1W 2) state is considered com-
pletely because of the original machine is starved from Md,x(1) point of view. The
second term of the right hand side, (S1S2), is the state in which the original machine
is idle because both coupled buffers are starved, thus from Md,x(1) point of view the
Pseudo machine is idle as well. The third term, (S1R2) is added because the original
machine is idle from the Md,x(1) point of view due to the starved coupled buffer (Bx1
or By1 or both are empty).
π(Rd,x(1)
)= π
(R1S2
)+ π (R) (3.29)
The remaining two state of the Markov chain of machine Ma represent the state in
54
3.4. TWO-LEVEL DECOMPOSITION APPROACH
which machine is locally failed and they are summed up to obtain the local down state
of the Md,x(1).
The aggregated steady state probabilities of the Pseudo machine Md,y(1) is treated in
the same fashion as the Md,x(1).
In order to obtain the state probabilities of the Pseudo Md,x(2), we need to aggregate
the Markovian state of the original machine in a following manner (the same aggregation
is applied for Md,y(2)):
π(W d,x(2)
)= π
(W 1W 2
)αa2 + π
(S1W 2
)(3.30)
π(W̄ d,x(2)
)= π
(W 1W 2
)αa1 (3.31)
π(Sd,x(2)
)= π
(W 1S2
)+ π
(S1S2
)+(R1S2
)(3.32)
π(Rd,x(2)
)= π
(S1R2
)+ π (R) (3.33)
Inputs to the BLD. Considering the steady state probabilities of the state transition
diagram depicted in Figure 3.11 for downstream Pseudo machines Md,x(i), i = 1, ..., 4,
the modified local failure pd,xt (i) and the competition failure and repair parameters
pd,xTx+1(i) and rd,xTx+1(i) can be obtained. Again, the modified local failure of the down-
stream Pseudo machines for each building block must be greater than the local failure
parameters of the original machine. This is because the assembly machine in the origi-
nal system might fail while it is processing the other coupled sub-assemblies. Also, the
failure probabilities of remote failure modes rd,xTa+1+j(i) and pd,xTa+1+j(i), i = 1, ..., 4 and
j = 1, ..., Ty can be derived, to be given in input to the BLD together with modified
local failure and competition failure parameters.
55
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
In order to obtain the modified local failure parameters of the downstream Pseudo
machine Md,x(1) by applying the balancing equation on node (Rd,xt (1)) of state transi-
tion diagram of Figure 3.11. Therefore, the local failure probability of Md,x(1) can be
obtained as:
pd,x,1t (i) =π(Rd,xi (1)
)π (W d,x(1))
rd,x,1t (i) i = 1, ..., Ta (3.34)
rd,x,1t (i) = ra(i) i = 1, ..., Ta (3.35)
Applying the balance equation on node (W̄ d,x(1)) we can derive the competition failure
parameters as written bellow:
pd,xTx+1(1) =π(W̄ d,x(1)
)π (W d,x(1))
rd,xTx+1(1) (3.36)
rd,xTx+1(1) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1
ps,d,1k (3.37)
The remote down states of the Pseudo machine Md,x(1) are those interruptions of flow
due to the empty buffer By1 which cause starvation of the Md,x(1). Thus, the following
can be written:
pd,xTa+1+i(1) = py,s,1i i = 1, ..., Ty (3.38)
rd,xTa+1+i(1) = ry,s,1i i = 1, ..., Ty (3.39)
The same reasoning is applied for the modified local failure, competition failure and the
remote failure and repair parameters of the other three downstream Pseudo machines.
For Md,x(2) the following equations are derived:
pd,x,2t (i) =π(Rd,xi (2)
)π (W d,x(2))
rd,x,2t (i) i = 1, ..., Ta (3.40)
rd,x,2t (i) = ra(i) i = 1, ..., Ta (3.41)
56
3.4. TWO-LEVEL DECOMPOSITION APPROACH
Applying the balance equation on node (W̄ d,x(2)) we can derive the competition failure
parameters as written bellow:
pd,xTx+1(2) =π(W̄ d,x(2)
)π (W d,x(2))
rd,xTx+1(2) (3.42)
rd,xTx+1(2) = αa2(1− P2) when P2 = 1− Pa −Tx+Ty∑k=1
ps,d,2k (3.43)
The remote down states of the Pseudo machine Md,x(2) are those interruptions of flow
due to the empty buffer By2 which cause starvation of the Md,x(2). Thus, the following
can be written:
pd,xTa+1+i(2) = py,s,2i i = 1, ..., Ty (3.44)
rd,xTa+1+i(2) = ry,s,2i i = 1, ..., Ty (3.45)
The failure and repair parameters of Md,y(1) are obtained as following:
pd,y,1t (i) =π(Rd,yi (1)
)π (W d,y(1))
rd,y,1t (i) i = 1, ..., Ta (3.46)
rd,y,1t (i) = ra(i) i = 1, ..., Ta (3.47)
Applying the balance equation on node (W̄ d,y(1)) we can derive the competition failure
parameters as written bellow:
pd,yTx+1(1) =π(W̄ d,y(1)
)π (W d,y(1))
rd,yTx+1(1) (3.48)
rd,yTx+1(1) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1
ps,d,1k (3.49)
The remote down states of the Pseudo machine Md,y(1) are those interruptions of flow
due to the empty buffer Bx1 which cause starvation of the Md,y(1). Thus, the following
57
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
can be written:
pd,yTa+1+i(1) = py,s,1i i = 1, ..., Tx (3.50)
rd,yTa+1+i(1) = rx,s,1i i = 1, ..., Tx (3.51)
The failure and repair parameters of Md,y(2) are obtained as following:
pd,y,2t (i) =π(Rd,yi (2)
)π (W d,y(2))
rd,y,2t (i) i = 1, ..., Ta (3.52)
rd,y,2t (i) = ra(i) i = 1, ..., Ta (3.53)
Applying the balance equation on node (W̄ d,y(2)) we can derive the competition failure
parameters as written bellow:
pd,yTx+1(2) =π(W̄ d,y(2)
)π (W d,y(2))
rd,yTx+1(2) (3.54)
rd,yTx+1(2) = αa1(1− P1) when P1 = 1− Pa −Tx+Ty∑k=1
ps,d,2k (3.55)
The remote down states of the Pseudo machine Md,y(2) are those interruptions of flow
due to the empty buffer Bx2 which cause starvation of the Md,y(2). Thus, the following
can be written:
pd,yTa+1+i(2) = py,s,2i i = 1, ..., Tx (3.56)
rd,yTa+1+i(2) = rx,s,2i i = 1, ..., Tx (3.57)
3.4.3 Algorithm
In this section we describe the details of the iterative algorithm applied to develop
the performance evaluation tool. The method is implemented in C++ and in the
next section we will illustrate the accuracy and reliability of the tool. The proposed
58
3.4. TWO-LEVEL DECOMPOSITION APPROACH
decomposition equations are solved by following an iterative algorithm inspired by DDX
algorithm that updates in sequence the parameters of the upstream and the downstream
pseudo-machines, by alternately visiting the MLD and the BLD.
1.initialization: For each Pseudo machine of each building block the local failures
are initialized to the values of the machines of the original system, while the remote
parameters and competition failure and repair probabilities are initialized to small
value, 0.05.
• For building block Mu,x(j) and Md,x(j), j=1,2
pu,xi (j) = pxi pu,xTx+1(j) = 0.05 i = 1, ..., Tx
ru,xi (j) = rxi ru,xTx+1(j) = 0.05 i = 1, ..., Tx (3.58)
pd,xi (j) = pai pu,xTa+1(j) = 0.05 i = 1, ..., Ta j = 1, 2
pd,xTa+1+k(j) = 0.05 k = 1, ..., Ty j = 1, 2
rd,xi (j) = rai ru,xTa+1(j) = 0.05 j = 1, 2
• For building block Mu,y(j) and Md,y(j), j=1,2
pu,yi (j) = pyi pd,yTy+1(j) = 0.05 i = 1, ..., Ty
ru,yi (j) = ryi rd,yTy+1(j) = 0.05 i = 1, ..., Ty
59
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
pd,yi (j) = pai pd,yTx+1(j) = 0.05 i = 1, ..., Ta j = 1, 2
pd,yTa+1+k(j) = 0.05 k = 1, ..., Tx j = 1, 2
rd,yi (j) = rai rd,yTx+1(j) = 0.05 j = 1, 2
Step 1 : Each building block is evaluated with the parameters updated in the previous
iteration (in the first iteration the initialized parameters all applied). Probabilities of
starvation, blocking and the average throughput of each building block is obtained with
the method proposed in Tolio et al. [2002]. Transition probabilities of the MLD for each
dedicated Markov model is updated referring to equations 3.10 and 3.11.
Step 2 : The failure parameters of Upstream Pseudo Machines and the Downstream
Pseudo Machines are evaluated as follows:
• Evaluation of steady state distribution of Markov model of manufacturing ma-
chines of the original system, Mx and My and the assembly machine Ma by
solving the linear equations of the discrete state-discrete time dedicated Markov
chains. The parameters for transition probabilities are taken from the results of
the building block evaluations in step 1.
• Aggregation of the states for two Pseudo machine Markov models, according to
equations 3.13, 3.14, 3.15, 3.16, 3.17, 3.18, 3.19 and 3.20 for upstream Pseudo
machines and 3.26, 3.27, 3.28, 3.29, 3.30, 3.31, 3.32 and 3.33 for down stream
Pseudo machines.
• Evaluation of modified local failures for upstream Pseudo machines of building
blocks representing the original machine Mx using equation 3.21 and for upstream
Pseudo machines of building blocks representing the original machine My using
equation 3.22 .
• Evaluation of modified local failures for downstream Pseudo machines of building
blocks representing the original machine Ma using equation 3.34.
60
3.5. NUMERICAL RESULTS
• Evaluation of remote failures of the downstream Pseudo machines for each build-
ing block using equations 3.38.
• Evaluation of competition failures of upstream Pseudo machines using equations
3.23 and 3.24 and for downstream pseudo machines by applying 3.36, 3.42, 3.48,
3.54.
• Substitution of failure and repair parameters (modified local failure, competition
failure and remote failure) to the step 1 for each building block.
The algorithm terminates when the conservation of flow condition becomes true:
| THx(i)− THy(i) |≤ ε for i = 1, 2
3.4.4 System Performance Measures
Following the algorithm, upon convergence, the system performance can be calculated
as:
THTot =
F∑i=1
THx(i) =
F∑i=1
THy(i);
Yi = (1− γai ) ∀i = 1, .., F
THEff =
F∑i=1
THx(i) · Yi;
Y System =THEff
THTot;
n̄xi = n̄x(i); n̄yi = n̄y(i); WIP =F∑i=1
n̄xi + n̄yi ;
3.5 Numerical Results
3.5.1 Accuracy testing
The accuracy of the proposed approximate analytical method is tested by comparing
the results with those provided by a Discrete Event Simulation (DES) model. The
61
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
simulation model is developed under the same manufacturing system assumptions. In
order to do so, we developed a DES model where the behavior of the machines is sim-
ulated under realistic system setting.
In order to characterize the simulation model, the sub-assembly key quality charac-
teristic measurements are sampled from the population distributions and are assigned
as attributes to the entities. Then, the sub-assemblies are sorted according to adopted
partitioning policy. After the component matching, the key quality characteristics
value of the assembled product is calculated and the non-conforming final assemblies
are identified and tagged by comparing this value with the predefined specification lim-
its. In this way, conforming final assemblies and non-conforming final assemblies in the
output flows are characterized and the generic system performance measures can be
estimated after a simulation run. In order to avoid the deadlock, the discard rule have
been taken into consideration as it was considered for the analytical model.
With R simulation replicates, the percentage error of the analytical method in the
estimation of the generic system performance measure, τ , versus simulation is estimated
by using the following equations:
τ̂Simulation =
∑Rr=1 τ
Simulationr
R(3.51)
ε(τ) =(τ̂Simulation − τanalytical)
τ̂Simulation
Given the large number of variables characterizing the considered problem, and the
consequent wide set of possible system configurations to be tested, we focus the nu-
merical analysis only on a sub-set of system configurations, that are representative of
the entire class of systems. The set of fixed parameters describing the analyzed system
configurations are reported in Table 3.3. The number of quality classes is set to C=2,
the consequent number of buffers is therefore F=2, equal width partitioning scheme for
sorting of sub-assemblies are adopted.
Regarding the assembly station, the quality characteristics of the assembled product
is the gap between components X and Y, i.e. z = x − y. The matching policy is
62
3.5. NUMERICAL RESULTS
Mx My Ma
X ∼ N(µx, σ2x) Y ∼ N(µy, σ
2y) Z = X − Y ; Z ∼ N(µx − µy, σ
2x + σ2
y)
µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126
LSLx=3.5 USLx=4.5 LSLy=2.8 USLy=3.8 LSLz=0.61 USLz=0.79
αx1=0.5 αx
2=0.5 αy1=0.5 αy
2=0.5 αa1 , αa
2 : factors
γx ≈ 0 γy ≈ 0
γ ≈ 0.4761 if F = 1,
γ1 = γ2 ≈ 0.2881 if F = 2
px, rx: factors py = 0, 01; ry = 0, 05 pa, ra: factors
Table 3.3: Summary of the adopted parameters.
a one-to-one matching between coupled buffers containing sub-assemblies X and Y.
The assembly policy is probabilistic depending on the available sub-assemblies in set of
coupled buffers. The reliability parameters of the manufacturing machine processing
component Y, My are fixed, while the reliability parameters of the other machines will
be modified to test systems with different bottleneck locations.
In order to generate different configurations to be tested, we adopted a Midpoint Latin
Hypercube Design approach, MLHD(80,9) with 9 factors and 80 runs. The ranges of
variability of the design factors are reported in Table 3.4. After generation of these
randomized 80 runs, we evaluate the performance of the system configurations with the
DES model and with the analytical method. Within the DES model, for each experi-
mental point we executed R=10 replicates of 1000000 time units with 100000 units of
warm up time, where the system statistics are not collected. The response of major
interest is the relative error of the analytical method towards simulation in the estima-
tion of the effective throughput and in the estimation of the total WIP. Therefore, for
each experimental point, two responses are obtained.
Parameter N1x N2
x N1y N2
y px rx pa ra α1a
Lower Bound 3 3 3 3 0.01 0.03 0.01 0.03 0.2
Upper Bound 30 30 30 30 0.1 0.3 0.1 0.3 0.8
Table 3.4: Range of variable parameters of accuracy test of analytical tool.
63
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
The results of this experimental plan are reported in Table 3.5. The method well cap-
tures the real system dynamics providing good estimates of the effective production
rate of the system.
In details, the average error of effective throughput over the 80 test cases is 1.07%, while
in the 90% of cases the error is below 3%. The method is accurate also while evaluating
the total WIP, with average estimation errors below 6% . It is worth to mention that
while the simulation requires about 8 hours to evaluate the 80 test systems the proposed
method requires 5 minutes for the entire experimental plan.
64
3.5
.N
UM
ER
ICA
LR
ES
ULT
S
ID Nx1 Nx
2 Ny1 Ny
2 px rx pa ra αa1 EEff
Sim EEffMet |ε%| WIPSim WIPMet |ε%|
1 7 13 10 25 0,077 0,275 0,063 0,258 0,459 0,50 0,51 2,03 13,57 12,77 -5,87
2 15 22 24 9 0,076 0,146 0,044 0,295 0,489 0,46 0,47 0,89 23,81 24,20 1,65
3 14 28 27 6 0,040 0,038 0,016 0,089 0,744 0,34 0,34 -0,32 29,08 31,12 7,02
4 18 28 24 26 0,014 0,187 0,012 0,062 0,391 0,55 0,52 -5,10 42,86 45,48 6,10
5 25 24 15 21 0,060 0,092 0,054 0,163 0,264 0,42 0,43 1,20 21,19 20,10 -5,16
6 22 12 29 4 0,023 0,157 0,032 0,254 0,354 0,55 0,56 1,77 28,26 27,11 -4,06
7 28 23 10 29 0,071 0,214 0,036 0,160 0,624 0,51 0,47 -8,24 22,36 21,22 -5,09
8 4 9 20 18 0,057 0,180 0,034 0,140 0,691 0,48 0,48 -0,60 18,69 18,77 0,41
9 9 9 30 19 0,027 0,170 0,022 0,170 0,759 0,55 0,56 1,82 19,15 20,11 4,99
10 15 11 10 21 0,094 0,140 0,041 0,076 0,339 0,38 0,38 -0,34 16,94 17,72 4,61
11 30 10 9 25 0,075 0,099 0,074 0,079 0,654 0,33 0,33 1,63 47,44 44,43 -6,35
12 24 19 29 27 0,089 0,133 0,025 0,268 0,571 0,42 0,42 -1,10 47,33 44,22 -6,57
13 14 7 5 14 0,016 0,035 0,070 0,200 0,406 0,40 0,41 3,49 23,03 22,20 -3,61
14 12 26 13 6 0,024 0,184 0,048 0,099 0,496 0,44 0,46 2,54 42,83 39,41 -7,99
15 5 24 21 24 0,072 0,292 0,045 0,265 0,474 0,53 0,54 1,87 33,56 30,24 -9,89
16 23 29 8 12 0,068 0,069 0,023 0,038 0,601 0,33 0,33 -1,30 30,45 27,26 -10,49
17 16 16 22 26 0,078 0,052 0,024 0,153 0,646 0,28 0,28 0,34 44,85 44,65 -0,45
18 8 21 25 13 0,053 0,268 0,067 0,234 0,361 0,51 0,53 3,02 37,65 34,52 -8,30
19 13 27 17 26 0,042 0,103 0,031 0,116 0,249 0,47 0,47 1,76 37,63 35,35 -6,06
20 8 18 22 8 0,062 0,032 0,061 0,133 0,669 0,23 0,23 0,99 30,47 29,26 -3,97
21 23 13 25 6 0,081 0,241 0,090 0,180 0,399 0,45 0,46 1,87 43,97 40,09 -8,81
22 12 30 9 29 0,066 0,082 0,075 0,281 0,661 0,39 0,39 0,75 35,59 33,94 -4,62
23 29 5 21 5 0,056 0,265 0,071 0,244 0,309 0,50 0,51 1,66 33,65 28,74 -14,58
24 4 14 6 22 0,032 0,065 0,093 0,055 0,256 0,24 0,25 2,79 35,53 34,60 -2,64
25 26 30 19 24 0,069 0,130 0,078 0,103 0,721 0,39 0,40 2,13 64,21 62,22 -3,09
26 19 15 27 16 0,036 0,173 0,065 0,130 0,714 0,45 0,47 2,84 47,22 45,25 -4,17
27 17 14 29 14 0,059 0,167 0,092 0,261 0,796 0,47 0,49 2,79 38,51 37,25 -3,27
65
3.
SE
LE
CT
IVE
AS
SE
MB
LY
SY
ST
EM
CO
NV
EN
TIO
NS
,S
YS
TE
MD
ES
CR
IPT
ION
AN
DA
NA
LY
TIC
AL
PE
RF
OR
MA
NC
EE
VA
LU
AT
ION
ME
TH
OD
OL
OG
Y
28 20 8 17 30 0,090 0,204 0,014 0,143 0,699 0,48 0,47 -2,30 36,93 33,33 -9,76
29 22 28 11 14 0,080 0,194 0,030 0,096 0,226 0,46 0,47 1,82 31,71 27,53 -13,18
30 7 10 23 17 0,093 0,136 0,098 0,197 0,534 0,39 0,39 1,23 38,68 36,90 -4,60
31 28 15 28 7 0,097 0,079 0,077 0,167 0,789 0,31 0,31 1,10 35,30 34,30 -2,85
32 4 27 18 12 0,079 0,221 0,052 0,285 0,504 0,49 0,49 1,33 26,80 24,21 -9,65
33 11 17 30 12 0,011 0,096 0,072 0,298 0,706 0,52 0,54 3,92 35,39 31,19 -11,88
34 8 20 8 29 0,012 0,197 0,043 0,248 0,241 0,53 0,55 2,84 25,34 23,35 -7,87
35 29 19 6 10 0,020 0,258 0,039 0,224 0,774 0,54 0,55 2,37 42,97 40,92 -4,77
36 6 23 12 11 0,029 0,062 0,027 0,241 0,736 0,46 0,46 1,22 21,07 18,58 -11,83
37 19 4 14 15 0,013 0,295 0,040 0,292 0,564 0,55 0,57 2,46 27,36 24,74 -9,55
38 20 18 16 23 0,041 0,045 0,013 0,042 0,436 0,35 0,35 -0,39 38,78 36,52 -5,84
39 20 5 13 7 0,035 0,251 0,051 0,113 0,376 0,45 0,46 1,99 30,68 27,42 -10,65
40 27 26 23 28 0,058 0,254 0,035 0,032 0,631 0,33 0,34 0,69 85,80 82,22 -4,18
41 5 15 5 5 0,095 0,059 0,096 0,251 0,211 0,25 0,26 2,16 10,39 9,82 -5,47
42 26 26 15 17 0,031 0,160 0,060 0,177 0,384 0,50 0,52 3,47 53,16 48,33 -9,08
43 16 12 12 4 0,033 0,285 0,085 0,126 0,729 0,39 0,41 4,17 30,72 29,60 -3,63
44 21 19 13 25 0,084 0,119 0,042 0,092 0,541 0,40 0,40 -0,29 41,25 38,09 -7,66
45 9 29 6 23 0,034 0,238 0,049 0,187 0,451 0,51 0,53 3,16 36,32 33,32 -8,26
46 17 5 21 9 0,021 0,177 0,080 0,106 0,481 0,39 0,40 1,87 40,07 37,61 -6,15
47 22 6 11 22 0,054 0,231 0,099 0,052 0,369 0,24 0,24 0,32 54,93 54,11 -1,49
48 30 4 7 20 0,083 0,234 0,056 0,065 0,751 0,35 0,36 1,78 44,46 43,19 -2,86
49 13 22 4 27 0,038 0,055 0,089 0,049 0,766 0,24 0,24 -0,08 53,79 51,46 -4,33
50 6 20 11 20 0,067 0,113 0,076 0,136 0,519 0,39 0,39 0,85 33,38 30,81 -7,71
51 5 8 20 30 0,063 0,200 0,062 0,072 0,781 0,36 0,36 -0,42 50,32 48,55 -3,51
52 19 25 27 15 0,045 0,150 0,095 0,146 0,444 0,42 0,43 1,25 65,28 62,07 -4,92
53 25 20 4 13 0,050 0,298 0,079 0,288 0,429 0,50 0,51 3,51 40,91 37,12 -9,25
54 21 6 28 18 0,098 0,217 0,094 0,123 0,324 0,39 0,39 0,29 54,10 51,35 -5,08
55 12 6 7 11 0,017 0,163 0,068 0,069 0,316 0,34 0,35 2,38 27,73 26,50 -4,42
66
3.5
.N
UM
ER
ICA
LR
ES
ULT
S
56 29 10 26 30 0,030 0,116 0,038 0,190 0,684 0,52 0,49 -5,81 44,28 40,34 -8,89
57 16 25 25 18 0,044 0,106 0,053 0,271 0,639 0,49 0,50 1,28 37,51 34,03 -9,28
58 30 7 28 11 0,061 0,271 0,088 0,119 0,526 0,40 0,41 1,62 59,77 56,24 -5,92
59 6 11 7 16 0,088 0,143 0,011 0,035 0,676 0,38 0,37 -3,19 21,08 20,34 -3,50
60 9 12 18 23 0,049 0,244 0,021 0,086 0,511 0,51 0,52 0,91 33,28 29,27 -12,03
61 23 7 15 15 0,043 0,072 0,050 0,059 0,549 0,34 0,34 0,83 39,40 35,94 -8,78
62 28 27 8 8 0,074 0,261 0,057 0,238 0,331 0,50 0,52 3,60 37,34 31,32 -16,13
63 24 23 20 28 0,048 0,042 0,015 0,150 0,579 0,33 0,33 -0,43 42,94 42,57 -0,87
64 11 24 22 20 0,085 0,278 0,069 0,214 0,286 0,49 0,51 2,38 38,22 35,42 -7,33
65 7 21 9 13 0,047 0,281 0,087 0,221 0,234 0,46 0,48 4,22 26,63 24,91 -6,45
66 27 17 19 10 0,052 0,153 0,017 0,194 0,616 0,51 0,52 1,61 24,80 21,70 -12,50
67 24 14 30 10 0,051 0,076 0,047 0,204 0,586 0,41 0,42 0,97 36,79 34,80 -5,41
68 10 22 16 19 0,025 0,086 0,033 0,278 0,346 0,51 0,53 2,33 27,35 23,87 -12,74
69 10 8 23 16 0,018 0,207 0,097 0,211 0,414 0,47 0,48 2,33 40,48 38,23 -5,56
70 11 11 16 24 0,015 0,248 0,066 0,275 0,594 0,54 0,56 3,38 35,92 31,91 -11,16
71 27 4 4 5 0,092 0,049 0,029 0,157 0,556 0,23 0,22 -6,18 9,03 8,22 -9,00
72 26 29 12 27 0,026 0,224 0,020 0,082 0,279 0,52 0,54 2,80 49,86 45,84 -8,07
73 18 30 26 22 0,086 0,288 0,059 0,045 0,301 0,31 0,31 0,94 79,35 77,94 -1,78
74 18 9 14 7 0,070 0,123 0,081 0,227 0,204 0,42 0,43 1,42 22,78 20,90 -8,23
75 10 16 5 28 0,087 0,190 0,084 0,109 0,421 0,38 0,38 1,39 40,46 38,25 -5,44
76 21 21 18 9 0,096 0,126 0,083 0,217 0,466 0,40 0,40 1,05 28,71 25,85 -9,95
77 25 13 14 21 0,022 0,089 0,026 0,207 0,294 0,53 0,55 2,26 31,76 30,22 -4,86
78 13 25 24 19 0,039 0,227 0,058 0,184 0,609 0,51 0,53 2,59 51,01 46,40 -9,04
79 14 18 19 8 0,099 0,211 0,086 0,231 0,219 0,45 0,46 1,89 28,76 26,66 -7,29
80 15 16 26 4 0,065 0,109 0,018 0,173 0,271 0,44 0,44 1,03 27,43 26,22 -4,41
Table 3.5: experimental results.
67
3. SELECTIVE ASSEMBLY SYSTEM CONVENTIONS, SYSTEMDESCRIPTION AND ANALYTICAL PERFORMANCE EVALUATIONMETHODOLOGY
68
4
Selective Assembly System
Analysis
4.1 Selective Assembly System Behavior
Given the good accuracy of the proposed approach, the method has been used to study
the system behavior of the selective assembly systems. In detail, two sets of experiments
have been conducted. First, the impact of the total buffer size on the total throughput,
effective throughput and WIP of the selective assembly system of two quality classes
is explored and the results are compared to those of the normal assembly system with
the same total buffer space. This experiment leads us to realize the benefits of the se-
lective assembly system comparing to the normal assembly system. Second, we studied
the behavior of the selective assembly system performance under increased number of
quality classes. Again in the second experiment, the total buffer size of the system is
fixed as the number of quality classes increases.
For both experiments, the same data as the previous experiments are considered, except
the machines reliability data. They are all set equal to the machine of the previous set
of tests (p = 0.01, r = 0.05). For the first experiment, since the reliability parameters
are identical, the total buffer space is equally distributed between the buffers in the
system. This is the best possible way to allocate buffers when the machines are iden-
tical. The total buffer size varies from 12 to 60, which means for each buffer the size
varies from 3 to 15 (N ix and N i
y for i = 1, 2). For the second experiment, we considered
69
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
the same total buffer space, 60, and we divide the total space by the number of quality
classes as it increases form 2 to 6.
Although the selective assembly system provides a higher system yield with respect
to the non-selective assembly system (from 52% to 71% which is approximately 36%
improvement), but it affects negatively the total throughput. As it is shown in Figure
4.1, the total throughput of the system is increasing in both normal assembly and se-
lective assembly systems as the total buffer space increases. But, due to the logistic
complexity of the selective assembly system the total throughput of this system is re-
duced compared to the non-selective assembly system. It is important to notice that,
because of the considered deadlock avoidance policy, discard policy, there are fraction
of manufactured sub-assemblies which are neglected by the manufacturing machines
and this leads to decreased total throughput. But, as it can be observed in the Figure
4.1, the negative effect of selective assembly system on the total throughput become
less evident as the total buffer space increases.
The combined result of increased yield and decreased total throughput is an increase of
the effective throughput with respect to the traditional, non-selective, assembly system,
as represented in Figure 4.2. This is because the weight of the increased yield is more
than the negative weight of the total throughput. In addition, the positive effect of
the selective assembly system on the effective throughput of the system is even more
visible as the total buffer size increases. For example, when the total buffer size is 12,
the effective throughput improvement comparing to the traditional assembly system is
18.17% while the improvement is 28.68% when the total buffer size increases to the 60.
Therefore, as the effective throughput is the performance measure which effectively il-
lustrate the benefits of one system comparing to the other, we can notice the remarkable
improvement of the selective assembly system comparing to the non-selective assembly
system.
Another result is the fact that the selective assembly system entails an average inventory
level increase comparing to the non-selective assembly system, as depicted in Figure
4.3. As mentioned earlier, the selective assembly system translates the system quality
issue into logistic performance issue. In fact, the price of more effective throughput is
70
4.1. SELECTIVE ASSEMBLY SYSTEM BEHAVIOR
Figure 4.1: Total throughput behavior as the total buffer space increases.
71
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
Figure 4.2: Effective throughput behavior as the total buffer space increases.
72
4.2. THE EFFECT OF MORE QUALITY CLASSES FOR SELECTIVEASSEMBLY SYSTEMS
Figure 4.3: WIP behavior as the total buffer size increases.
paid by the more average system work in progress. The increased WIP is more evident
as the total buffer space is increased.
4.2 The Effect of More Quality Classes for Selective As-
sembly Systems
In this thesis the analytical performance evaluation tool is provided for two quality
classes and the accuracy of the tool is tested comparing to simulation results of the
same configuration model. The extension of the analytical model of two quality class
model to more quality classes is straightforward with the same provided framework.
But we applied the developed discrete event simulation model to analyze the selective
assembly systems under more quality classes. In details, we studied the effect of the
number of quality classes on the system yield, the total throughput, and the effective
throughput.
73
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
Mx My Ma
X ∼ N(µx, σ2x) Y ∼ N(µy, σ
2y) Z = X − Y ; Z ∼ N(µx − µy, σ
2x + σ2
y)
µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126
LSLx=3.5 USLx=4.5 LSLy=2.8 USLy=3.8 LSLz=0.61 USLz=0.79
px = 0, 01; rx = 0, 05 py = 0, 01; ry = 0, 05 px = 0, 01; rx = 0, 05
Table 4.1: Summary of the adopted parameters for more quality classes test.
The complexity of the selective assembly logistic system increases by the increase in
number of quality classes, but the yield is expected to increase at the same time. The
increased logistic system complexity leads to degraded productivity of the system, re-
sulting in decreased total throughput. On the other hand, the more quality classes im-
proves the final assembly quality because the sub-assemblies are categorized in tighter
quality classes respecting their key quality characteristics. It must be noticed that, the
interaction effect of yield and total throughput is observed as the effective throughput,
which is the supporting performance measure of system management decision making
process.
The machine reliability parameters for this set of experiments are presented in Table 4.1
together with the distributions of key quality characteristics of sub-assemblies. Since
the reliability parameters are identical, the total buffer space of 60 is equally distributed
between the buffers in the system. This is the most effective way to allocate buffers
when the machines are identical.
For more than two quality classes of selective assembly systems we must take into con-
sideration a specific partition scheme. As mentioned earlier, There are two type of
partitioning scheme, the equal width and the equal probability scheme. For this partic-
ular system study we have considered the equal probability scheme. Equal probability
provides the better system performance in terms of productivity due to the lower level
of surplus sub-assemblies when the distribution variations are dissimilar, as discussed
earlier. The detailed partitioning for quality classes (from 2 classes to 6 classes) is
provided in Table 4.2.
74
4.2. THE EFFECT OF MORE QUALITY CLASSES FOR SELECTIVEASSEMBLY SYSTEMS
Sub-Assembly
X Y
Number of Quality Classes Limits LSL USL LSL USL
2Class 1 3,5 4 2,8 3,3
Class 2 4 4,5 3,3 3,8
3
Class 1 3,5 3,950036 2,8 3,278464
Class 2 3,950036 4,049964 3,278464 3,321536
Class 3 4,049964 4,5 3,321536 3,8
4
Class 1 3,5 3,921759 2,8 3,266276
Class 2 3,921759 4 3,266276 3,3
Class 3 4 4,078241 3,3 3,333724
Class 4 4,078241 4,5 3,333724 3,8
5
Class 1 3,5 3,902372 2,8 3,257919
Class 2 3,902372 3,970612 3,257919 3,287333
Class 3 3,970612 4,029388 3,287333 3,312667
Class 4 4,029388 4,097628 3,312667 3,342081
Class 5 4,097628 4,5 3,342081 3,8
6
Class 1 3,5 3,887779 2,8 3,251629
Class 2 3,887779 3,950036 3,251629 3,278464
Class 3 3,950036 4 3,278464 3,3
Class 4 4 4,049964 3,3 3,321536
Class 5 4,049964 4,112221 3,321536 3,348371
Class 6 4,112221 4,5 3,348371 3,8
Table 4.2: Partitioning limits for equal probability scheme.
Table 4.3 provides the performance measures of the interest for the selective assembly
system of 1 class (which represents the normal assembly) to 6 classes. For the nor-
mal assembly system and the selective assembly system of two quality classes, we have
applied our analytical method, while the results of the selective assembly of 3 quality
classes to 6 quality classes, are provided by running the developed simulation model
for 10 replicates of approximately 10000000 time units of operation. 95% confidence
interval widths are 0.01% , 0.01%, and 1.7% of the average effective throughput, aver-
age total throughput and the WIP, respectively.
75
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
Figure 4.4: Total TH behavior as the number of quality classes increases.
In the Figure 4.4 we illustrate the effect of increasing the number of quality classes on
the total throughput, as the total buffer space is fixed. As it is shown, the increasing
number of quality classes decreases the total throughput (the production rate of both
conforming and non-conforming sub-assemblies). This behavior is due to the additional
imposed complexity to logistic systems as the number of quality classes increases. In
the other words, the material flow complexity is increased by the number of quality
classes. This is because, the upstream manufacturing machines are regulating to place
the processed sub-assemblies into more buffers comparing to the less quality classes.
In fact, the more quality classes to distribute the processed sub-assemblies cause the
lower average buffer level for each sub-assembly in the particular buffer. From the
other hand, the assembly machine only selects the sub-assemblies from the available
coupled buffers. Therefore, the assembly machine remains starved more frequently as
the number of quality classes increases. This causes the lower level of total throughput.
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4.2. THE EFFECT OF MORE QUALITY CLASSES FOR SELECTIVEASSEMBLY SYSTEMS
For example, the total throughput of the designed selective assembly system with 6
quality classes are reduced comparing to the 2 quality classes by approximately 18%.
Number Of Classes TH-Total TH-Eff Yield
1 0,68 0,36 0,52
2 0,65 0,46 0,71
3 0,62 0,48 0,77
4 0,59 0,47 0,80
5 0,56 0,46 0,82
6 0,55 0,46 0,83
Table 4.3: Performance measures as the number number of quality classes increases.
Although the total throughput is reduced by the number of quality classes, the system
yield is increased as shown in Figure 4.6, as the number of quality classes increases. As a
result of this competing effect, the effective throughput curve is concave, it is increasing
until a certain point and then it starts decreasing (as it is shown in Figure 4.5). Thus,
being concern with the concave behavior of the effective throughput curve, it illustrates
that there is an optimal point to select for the number of quality classes. Therefore,
in order to make a proper decision for design of selective assembly systems in terms
of number of quality classes, there is an absolute need to observe the trad-off between
the logistic complexity and the system yield through the resulting effective throughput.
As mentioned in the previous chapter, the deadlock state is a consequence of system
complexity. In order to avoid the deadlock state, we have considered the discard policy,
both in our analytical method for two quality classes and in the simulation model of
more quality classes. In discard policy, when the manufacturing machines face a full
downstream buffer, they continue the production and if the sub-assembly belongs to the
full buffer it will be discarded. In the other words, discard policy avoids the deadlock
state by imposing the cost of neglecting conforming sub-assemblies. In our model,
both analytical model of two class system and the simulation models for extended
classes, we have considered the discard policy. Although selective assembly systems are
introduced to increase the quality of final assembly at the reduced cost, but discarding
the conforming sub-assemblies seems not economical for the practitioner. Therefore,
77
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
Figure 4.5: The effective throughput behavior as the number of quality classes increases.
we have introduced the new analytical approach to reduce the discard rate by applying
the process adaptation. In the next chapter we will describe the proposed method in
addition to other new flow control policies to design more efficiently selective assembly
systems for practitioners.
78
4.2. THE EFFECT OF MORE QUALITY CLASSES FOR SELECTIVEASSEMBLY SYSTEMS
Figure 4.6: System Yield behavior as the number of quality classes increases.
79
4. SELECTIVE ASSEMBLY SYSTEM ANALYSIS
80
5
Selective and Adaptive Assembly
Systems
5.1 Selective and Adaptive Assembly Systems Definition
Selective and Adaptive Assembly Systems are considered a different approach to im-
prove the quality of the assembled product. The selective part of Selective and Adaptive
Assembly Systems is characterized by the assembly of sub-assemblies based on match-
ing predetermined classification groups as introduced earlier. While the adaptive part
of selective and adaptive assembly systems is characterized by the control of process
parameters in the upstream component manufacturing processes. In fact, in Selective
and Adaptive Assembly Systems the term ”Adaptive” refers to the adaptation of the
target nominal value of the sub-assembly’s key quality characteristic in the upstream
sub-assembly manufacturing processes. This term is denoted as “process mean shift” as
well. By applying these principles, Selective and Adaptive Assembly Systems support
the assembly of high precision products from relatively low precision sub-assemblies, at
the cost of increasing the system complexity and decreasing the logistic performance of
the system.
There are studies that investigate the effects of the adaptability of processes on the
performance of Selective and Adaptive Assembly Systems, in addition to selective
assembly. Selective and Adaptive Assembly Systems productivity simulation results
Herrmann et al. [2010] give insight regarding the inter-dependencies of logistic system
81
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
design, production system design, and product design in determining the overall effi-
ciency of selective and adaptive assembly systems.
In Matsuura and Shinozaki [2011a] a one-shift process mean design for selective and
adaptive assembly systems was proposed. In details, by producing the component at
different target process means, each one having an assigned probability, the original
key characteristic distribution of the component was changed and controlled. The
authors show that with one shift in the process mean and the equal-probability par-
titioning scheme, zero surplus components can be obtained at the cost of highly in-
creasing the number of bins. The authors discussed the problem of determining the
optimal mean shift (the adaptation magnitude and frequency) for both equal width and
equal probability partitioning schemes when the sub-assembly with smaller variance is
manufactured at two shifted means and a tolerance constraint on the clearance is given.
The effects of mean shift on manufacturing mating components and the selection of
the number of bins in selective assembly through Taguchi loss function have also re-
ceived attention Kannan et al. [2008]. For the analysis of component tolerances it is
concluded that very lowest possible clearance variation with the loss function of zero
can be achieved when the mating sub-assembly tolerances are equal.
In Matsuura and Shinozaki [2011b], three-shifts process mean designs were investigated
to reduce the number of surplus components, as shown in Figure 5.1, where the process
adaptation is applied to the process of sub-assembly manufacturing with smaller varia-
tion level. In their paper, author proposed an optimal manufacturing mean design that
minimizes the number of surplus components when equal width partitioning scheme
has been applied. They demonstrated that the use of the proposed optimal process
mean shift design significantly reduces the number of surplus components compared
with the no-shift design.
When there is a large difference between the process variation of two sub-assemblies,
equal width partitioning will result in a large number of surplus sub-assemblies and
equal probability partitioning will result in some rejected products due to the improper
partitioning width design. In Matsuura and Shinozaki [2011a] authors proposed a
82
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Figure 5.1: Three shift policy for adaptive production systems.
method to determine the optimal process mean shift for both equal width and equal
probability in such a way that the surplus sub-assemblies are minimized. They have
shown that in some cases it is possible to achieve the zero level of surplus sub-assemblies
under equal probability partitioning scheme, with the cost of increased number of par-
titioning classes compare to the equal width partitioning scheme. Authors in Kannan
and Jayabalan [2002] and Kannan et al. [1997] proposed a method of manufacturing
components with smaller process variation at several shifted means. In Matsuura and
Shinozaki [2011a] they have shown their method is out-performing the method pro-
posed in Kannan and Jayabalan [2002].
As discussed above, although the process adaptability of selective and adaptive as-
sembly systems has been proposed as a suitable solution to improve the system per-
formance, the optimal number of process mean adjustment to minimize the surplus
sub-assemblies have not being considered. Furthermore, the effect of optimal adapt-
ability policies on the overall system performance of selective and adaptive assembly
systems received a limited attention. This is important because the effect of surplus
reduction (through several proposed models) need to be analyzed while the policy is
applied in the system with real settings, i.e., unreliable machines and limited buffers.
This is because, the surplus sub-assemblies are those who accumulate in limited capac-
ity buffers and cause the blocking phenomena for the manufacturing machines. This
83
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
phenomena has been neglected in the previous works by considering the unlimited
buffer capacities that are impractical in real system settings. In the other words, the
importance of the surplus sub-assemblies is underestimated by considering it as the
sub-assemblies which are left with no coupled sub-assemblies, while the main negative
effect is the cause to blocking phenomena. Consequently, it is derived that the surplus
sub-assemblies are the main drive for deadlock phenomenon and the the consequent
discarded sub-assemblies.
As mentioned above, the process mean adjustment might improve the system perfor-
mance by reducing the surplus sub-assemblies. But, process adaptability can be applied
to reduce the discard rate of sub-assemblies in deadlock states as well. As we have men-
tioned in previous chapter, we have applied the discard policy to avoid the deadlock
state for developing the analytical methods. The discard rate of sub-assemblies while
the discard policy is applied could be unacceptable for the practitioner, as mentioned
earlier. Therefore, we have imposed the adaptability of manufacturing process into
selective assembly systems in order to reduce the discard rate.
In this chapter, first we describe our extended analytical performance evaluation method
of selective assembly systems including the new adaptability policy to reduce the dis-
card rate of sub-assemblies. Then, we describe our optimal adaptability design method
which contributes to minimize the surplus sub-assemblies. The effect of proposed pro-
cess adaptability on the system performance of the selective and adaptive assembly
systems with realistic system setting is described later. Finally we compared the re-
sults of the proposed optimal shift design method to that of previous versions.
5.1.1 Process Adaptability Approach To Reduce The Discard Rate:
Analytical Approach
The discard policy which is applied in the performance evaluation of selective assem-
bly systems caused a large number of sub-assemblies to be neglected. The discard is
ruled when the upstream manufacturing machines face one of the buffers full and they
randomly produce the sub-assembly to be placed in the full buffer. In fact, the dis-
carded sub-assembly is a conforming sub-assembly which is neglected due to the logistic
84
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
complexity of the system. Therefore, we have proposed a method to reduce the the
discard rate. In the literature, the process adaptability is imposed to the process mean
with the determined probability. While we proposed to adjust the process mean of the
manufacturing process with smaller variation only when one of the buffers of the
machine is full. In the other words, the process is adapted to another process mean
only when it is needed based on the buffer levels.
In order to extend our analytical performance evaluation model, we need to include
the process adjustment for the manufacturing machine of the more capable process.
We have considered the My machine to be the more capable manufacturing machine.
Therefore we need to modify the Markov model of the My in machine level decompo-
sition algorithm. In the following we describe the required modifications.
5.1.1.1 Sub-assembly Manufacturing Machine My
We assume the process adjustment requires negligible set-up times (only process target
adjustments). A shift τ modifies the process mean level µy(τ) = µy + δ(τ). Therefore,
it affects the sorting probabilities of the component y in the downstream buffers as
follows:
αy(τ)i =
∫ Lxi
lxi
Fx(τ)(s)ds ∀i = 1, .., F (5.1)
where Fy(τ) is the cumulative probability function of the shifted distributions with
mean µy(τ) and standard deviation σy. The fraction of components y produced under
the target process mean µy(τ) is denoted as ϑi(τ). Since it involves a change in the
quality feature distribution of one component, the process adaptation modifies the as-
sembly yield. Under process shift τ , the adjusted fraction of non-conforming assembled
products for flow i is γai (τ) which obviously differs from the non-adjusted process mean.
State Transition Diagram. Depending on the level of the adjacent buffers, ma-
chine My behaves as reported in Table 5.1. As it can be noticed, the discard policy
affects the behavior of the machine in the states where one of the two buffer is full and
the other is not full (row 1 to row 4). In these conditions, process adjustment can be
85
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Buffers Part qualityMachine State
Discard Rule
Bx1 By
2 Class Output
Buffer
Prob.
Not Full Full 1 UP(W 1B2) By1 α
y(τ)1
Not Full Full 2 UP(W 1B2) discard αy(τ)2
Full Not Full 1 UP(B1W 2) discard αy(τ)1
Full Not Full 2 UP(B1W 2) By2 α
x(τ)2
Not Full Not Full 1 UP(W 1W 2) By1 αy1
Not Full Not Full 2 UP(W 1W 2) By2 αy2
Full Full 1-2 BL(B1B2) / /
Not Full Full 1-2 DOWN(RB2) / /
Full Not Full 1-2 DOWN(B1R) / /
Not Full Not Full 1-2 DOWN(R) / /
Table 5.1: Behavior of machine My. ”B” denotes blocking states, ”W” denotes opera-
tional states, and ”R” denotes down states.
activated and the sorting probabilities are dependent on the shift entity δk, as expressed
in equation (5.1). The Markov chain representing the behavior of the component man-
ufacturing machine My is represented in Figure 5.2 (to simplify the picture, transition
probability p̄ is shown instead of 1 − p; moreover P1 =∑Ty
t=1 pyt +
∑Ta+1+Txk py,b,1k ).
The probability of failure and repair of machine My, i.e. py and ry, are known since
they are input data of the problem. The probabilities of transition to blocking states
are unknown but have been derived in the BLD similar to the non-adjustable model
presented in “Selective Assembly System Conventions, System Description and Ana-
lytical Performance Evaluation Methodology” chapter. Therefore, all the transition
probabilities in this Markov chain are known.
Machine Level Analysis. By analyzing the Markov chain in Figure 5.2, the steady-
state probabilities of Markov chain characterizing the My behavior can be derived.
Then, its behavior is approximated by simplified multiple failure machine models of
the upstream pseudo-machines Mu,y(i), i = 1, 2. The Markov chain in Figure 5.2 can
be solved and the steady-state probabilities can be calculated. Then, the Markov model
representing the My behavior is transformed into the Markov chain represented in Fig-
86
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Figure 5.2: Markov model characterizing the Machine Y, My, with process adjustments.
87
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Figure 5.3: Pseudo machine state transition diagram.
ure 5.3 which is similar to that of manufacturing machine with no process adjustment.
The transformation is made through the re-distribution of the calculated steady-state
probabilities, performed by using the following State Aggregation Equations: For ex-
ample, for Mu,y(1), the following equations are adopted (π(· · · ) is representing the
steady-state probability of the state in brackets):
π (W u,y(1)) = π(W 1W 2
)αy1 + π
(W 1B2
)αy(τ)1 (5.2)
π(W̄ u,y(1)
)= π
(W 1W 2
)αy2 + π
(W 1B2
)αy(τ)2 (5.3)
π (Bu,y(1)) = π(B1W 2
)+ π
(B1B2
)+ π(B1R2) (5.4)
π (Ru,y(1)) = π(R1B2
)+ π (R) (5.5)
Similar equations apply to Mu,y(2). From the point of view of the material flow
entering buffer By1 , the throughput of scrapped of parts due to the discard policy
(π(W 1B2
)αy(τ)2 ) can be seen as an interruption of flow due to the competition failure
state W̄ u,y(1). Moreover, the fraction ϑi(τ) of parts produced under the target process
mean µy(τ) can be computed as:
ϑ1(τ) =π(W 1B2)α
x(τ)1
π(W u,x(1))ϑ2(τ) =
π(B1W 2)αx(τ)2
π(W u,x(2))(5.6)
88
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Inputs to the BLD. With similar approach we need to transfer the machine failures
to the upstream Pseudo machines which represent the My. The probability of Mu,y(i)
failing in local mode can be obtained as:
pu,yt (1) =π (Ru,yt (1))
π (W u,y(1))ru,yt (1) t = 1, .., Ty (5.7)
The probabilities of failure and repair for the competition failure mode can be derived
as follows:
pu,yTx+1(1) =π(W̄ u,y(1)
)π (W u,y(1))
ru,yTy+1(1) (5.8)
ru,yTy+1(1) = αy1(1−Ty∑t=1
pyt )
5.1.1.2 The Effect of Process Adaptation On the System Performance
The system parameters is presented in Table 5.2. .The buffer sizes are all set to 3 and
this is because the machines reliability are the same and the equal buffer size is the
best approach for buffer allocation in this particular system configuration . If By1 is
full, the target mean of the more capable process My is shifted to µy(τ) = µy + δ.
Results are reported in Figure 5.4. As it can be noticed, the shift has a double effect
on the performance of the system. On the one hand, it increases the total production
rate of the system, by decreasing the probability of producing a quality class i part
when buffer Byi is full. On the other hand, by increasing the shift, the yield increases
up to a certain level, and then it decreases. As a result of this competing effects, the
effective production rate is a concave function that is maximized for a certain value
of the shift entity δ = 0.07. For this level, the effective throughput of the system is
consistently higher than the effective throughput without process adaptation (δ = 0).
It is worth to mention that, in the proposed case, the yield is maximized for δ = 0.056.
This means that a methodology that neglects the interactions between quality and
production logistics, only provides sub-performing configurations of the system.
5.1.2 The Optimal Process Shift Design in Selective and Adaptive
Assembly Systems
In this section we address the problem of optimally selecting the number of shifts of pro-
cess mean in selective and adaptive assembly systems. Moreover, we will demonstrate
89
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Mx My Ma
X ∼ N(µx, σ2x) Y ∼ N(µy, σ
2y) Z = X −Y ; Z ∼ N(µx−µy, σ
2x +σ2
y)
µx=4; σx=0.116 µy=3.3; σy=0.05 µz=0.7; σz=0.126
LSLx=3.5 USLx=4.5 LSLy=2.8 USLy=3.8 LSLz=0.61 USLz=0.79
αx1=0.5 αx
2=0.5 αy1=0.5 αy
2=0.5 αa1 , αa
2 : 0.5
γx ≈ 0 γy ≈ 0
γ ≈ 0.4761 if F = 1,
γ1 = γ2 ≈ 0.2881 if F = 2
px = 0, 01, rx = 0, 05 py = 0, 01; ry = 0, 05 pa = 0, 01, ra = 0, 05
Table 5.2: Summary of the adopted parameters.
Figure 5.4: Effect of Shifts on System performance.
90
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
the effect of the proposed optimal design on the throughput and logistics performance
of the system, showing great benefits towards state-of-the-art approaches.
5.1.2.1 Modeling Assumptions
Sub-assembly key characteristics distribution. We assume the assembly of two
sub-assemblies, namely X and Y. The key quality characteristic of sub-assembly X,
named x, is assumed to be normally distributed, i.e. N(µx, σx). The key quality char-
acteristic of sub-assembly Y, namely y, is assumed to be normally distributed with
mean µy and variance σ2y = (τσx)2, where τ is the ratio between the standard devia-
tion of Y and X, 0 ≤ τ ≤ 1. The clearance between the two components is C with
tolerance ∆ (the acceptable clearance range is within C ±∆). The process mean shift
(the magnitude of the process adjustment) is assumed to be applicable only to the low-
est variance component Y. Each shift is defined by a process mean shift magnitude of bi
from the nominal process mean µy and an associated shift probability of pi. Symmet-
ric process mean shifts to right and left are assumed, i.e. each shift with magnitude bi
has a corresponding shift with magnitude −bi, both having probability pi of occurrence.
The total number of process target values is denoted with S and the corresponding
shift levels and probabilities are the element of the vectors b and p. In this settings,
S = 1 means that there is unique process target value, i.e. no shift is implemented.
The overall component distribution is built as the probability-weighted sum of shifted
distributions. Figure 5.5 shows a distribution for a five-shift design.
The fraction of components X and Y that is out of specification limits is denoted
respectively as γx and γy. These fractions can be calculated as:
γx = probability{x<LSLx ∪ x>USLx} (5.9)
γy = probability{y<LSLy ∪ y>USLy}
where the LSL and the USL are respectively the lower and the upper specification
limits imposed on the sub-assemblies by design. We assume that out of specification
sub-assemblies are scrapped by the measurement stations prior to the classifications.
91
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Figure 5.5: Five symmetric shifts of process mean for Y.
Partitioning Scheme. Sub-assemblies are partitioned according to the equal-width
partitioning scheme. The width of each partition is w = 2D/n, where 2D=USL-LSL.
The number of bins n can be chosen to have 0 ≤ w ≤ ∆, i.e. all the coupled sub-
assemblies are within the acceptable clearance range thus being conforming assembled
parts. In this model, design specification widths are assumed to be equal for both
components, Dx = Dy = D. Clustering bins are built as follows:
(x0, x1, ..., xn−1, xn) = (µx −D,µx −D + w, ..., µx +D − w, µx +D) (5.10)
(y0, y1, ..., yn−1, yn) = (µy −D,µy −D + w, ..., µy +D − w, µy +D)
where, (xi−1, xi] and (yi−1, yi] are the boundaries of each partition i = 1, .., n for com-
ponent X and component Y, respectively.
Performance Measures. The performance measures of interest for optimal shifts
design are considered as follows:
• R(S, b, p) is the matching probability, i.e. the probability of matching compo-
nents X and Y of corresponding buffers, under S process mean levels and shift
parameters b and p.
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5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
• TH is the average throughput of the system, i.e. the number of parts produced
in a time unit. In this model the THTot = THEff = TH. This is because
the number of quality classes are considered so that all the assembled parts are
conforming after assembly process.
• WIP is the average level of work-in-progress, i.e. the total number of components
X and Y waiting in bins for assembly.
5.1.2.2 Matching Probability Evaluation Method
To evaluate the matching probability R(S, b, p), we set Ri(S, b, p) as the probability of
matching sub-assembly X and Y for partition i, where i = 1, .., n. The probability PX,i
of releasing a component X in partition i is:
PX,i = FX(Xi)− FX(Xi−1) (5.11)
FX = Φ ((X − µx)/σx)
Where Φ(x) is the standard cumulative normal distribution. Similarly, the probability
of releasing component Y in partition i, PY,i, is:
PY,i = FY (Yi)− FY (Yi−1) (5.12)
In case S shifts are implemented to the target mean of sub-assembly Y, the cumulative
distribution function of Y is:
FY (y) =(1− 2
(S−1)/2∑i=1
Pi)Φ((y − µy)/σy)+ (5.13)
(S−1)/2∑i=1
Pi [Φ(y − µy − bi)/σy + Φ((y − µy + bi)/σy)]
Therefore, the matching probability of each partition is:
Ri(S, b̄, p̄) = Min{FX(Xi)− FX(Xi−1), FY (Yi)− FY (Yi−1)} (5.14)
and the total matching probability is:
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5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
R(S, b̄, p̄) =
n∑i=1
Ri(S, b̄, p̄) (5.15)
It is worth to mention that there exists a limit value of this matching probability, called
Rlim, which is related to the fraction of scrapped components as follows:
Rlim = min {1− γx, 1− γy} (5.16)
The corresponding number of shifts is Slim. It is remarkable to notice that increasing
the number of shifts beyond Slim does not provide any additional contribution to the
matching probability increase.
5.1.2.3 Shift Design Optimization
Formulation of optimization problems. In order to derive the optimal shift design
of selective and adaptive assembly systems, two optimization problems are formulated
and solved.
Problem 1: Maximization of the matching probability
The objective is to find the maximum matching probability R(S, b, p), for a given value
of S. The decision variables are b and p for the corresponding value of S. The following
constraint optimization problem is solved:
max.x
R(S, b, p)
s.t. pi ≥ 0 ∀i = 1, ..., (S − 1)/2
1− 2
(S−1)/2∑i=1
Pi ≥ 0
b1 ≤ b2 ≤ ... ≤ b(S−1)/2
(5.17)
The first and second constraints impose that the probabilities of each shift must be
non-negative. The third constraint imposes that each shift magnitude must be larger
than the previous one.
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5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Figure 5.6: Block Diagram for Problme 2.
Problem 2: Optimal number of shifts
The objective is to find the optimal number of shifts S* which corresponds to a required
target matching probability R*(S,b,p). The formulation of problem 2 is:
min.s
S
s.t. R(S, b̄, p̄) ≥ R∗(S, b̄, p̄)(5.18)
Solution of the Optimization Problem. The method used to solve problem 1 is
inspired by Matsuura and Shinozaki [2011b] and is based on non-linear optimization.
While approaching problem 2, we first check the existence of a feasible solution to
the problem. The required matching probability R∗ should be lower than the overall
maximum matching probability Rlim. If this condition holds, the solution of Problem
2 is found by applying the algorithm described in Figure 5.6. If the required match-
ing probability R∗ is attained with no shift (S = 1) of process Y, there is no need to
adapt the process. Otherwise, we increase the number of shifts (S = S + 2) and we
solve Problem 1 to find the maximal attainable matching probability with the updated
number of shifts. This procedure is repeated until the target matching probability is
met. The corresponding shift value solves Problem 2.
95
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Upon convergence, the vectors b and p contain the optimal design of the process shift
levels and the associated probabilities.
Numerical Results. In the following, two numerical examples that show the benefits
of the proposed approach with respect to state of the art process shift design methods
are extensively reported. In both the cases the required matching probability, R∗, is
set to 99%. The sample case data are reported in Table 5.3.
ParametersExperiments
1 2
µx 4 2.75
σx 0.116 0.15
µy 3.3 2.5
σy 0.05 0.045
D 0.35 0.45
n 8 10
D ±∆ 0.7± 0.09 0.25± 0.09
Table 5.3: Sample case data.
Case 1. Based on the reject fractions of components X and Y, the overall maximum
matching probability Rlim is 99.73%, which is higher than required matching probabil-
ity. Applying the procedure explained in the previous section solves Problem 2. Table
5.4 shows the maximum matching probability for increasing process adaptation levels.
As it can be observed, for 5 target levels, the maximum matching probability of 99.7%
meets the required matching probability of 99%, demonstrating that with our method
it is possible to achieve the required matching probability R∗.
If compared to the existing methods to support 3-shift process design developed in Mat-
suura and Shinozaki [2011b] and Kannan and Jayabalan [2002], the proposed method
shows marked improvement in terms of matching probability. There is a 1.7% improve-
ment of matching probability of the proposed optimal 5-shift design towards the 3-shifts
design proposed by Matsuura and Shinozaki [2011b] and 8.5% improvement compared
to the 3-shift design of Kannan and Jayabalan [2002]. It is worth highlighting that
96
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Iteration Shift Matching Probability
1 1 62.68%
2 3 98%
3 5 99.73%
4 7 99.73%
5 9 99.73%
Table 5.4: Maximum matching probability for a given number of shifts in Case 1.
Figure 5.7: Matching probability as a function of the number of shifts - Case 1.
the methods proposed in Matsuura and Shinozaki [2011b] and Kannan and Jayabalan
[2002] do not allow to meet the matching probability requirement. Figure 5.7 graphi-
cally depicts the improvements of our method compared to these previous designs.
Table 5.5 illustrates the details of the partitioning design and the corresponding match-
ing probabilities when the process is not adapted, i.e. no shift is applied. As it can be
noticed, by adapting the process target values according to the optimal process shift
design proposed in this paper an increase of the matching probability of about 60%
in the matching probability is met towards the case where no adaptation is applied.
This practically means a consistent reduction of the work in progress and a consistent
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5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
increase in the system throughput. Table 5.6 illustrates the specific results of the meth-
ods proposed by Matsuura and Shinozaki [2011b] and Kannan and Jayabalan [2002]
and the proposed optimal shift design.
Bin number
Partitioning Probabilities
X YX Y Ri
Min Max Min Max
3.65 2.95 0.00 0.00
1 3.65 3.74 2.95 3.04 0.01 0.00 0.00
2 3.74 3.83 3.04 3.13 0.05 0.00 0.00
3 3.83 3.91 3.13 3.21 0.16 0.04 0.04
4 3.91 4.00 3.21 3.30 0.27 0.46 0.27
5 4.00 4.09 3.30 3.39 0.27 0.46 0.27
6 4.09 4.18 3.39 3.48 0.16 0.04 0.04
7 4.18 4.26 3.48 3.56 0.05 0.00 0.00
8 4.26 4.35 3.56 3.65 0.01 0.00 0.00
4.35 3.65 0.00 0.00
Matching 0.627
Surplus 0.371
Table 5.5: Binning and probabilities for Case 1, without process adaptation.
Case 2. Experiment 2 differs from experiment 1 since the capability of the process that
produces component Y is higher. The results for Case 2 are given in Table 5.7. Again,
a five-shift design results to be optimal in these settings. As it can be seen from Table
5.7, there is 5.7% improvement in terms of matching probability between the 3-shifts
design proposed by Matsuura and Shinozaki [2011b] and our optimal 5-shifts design.
The matching probability improvement of our optimal design compared to the 3-shifts
design proposed by Kannan and Jayabalan [2002] is about 19%. Figure 5.8 shows the
impact of increasing shift on the matching probability for Case 2. Table 5.8 illustrates
the details of the partitioning design and the corresponding matching probabilities
when the process is not adapted. Again, it can be noticed that by adapting the process
target values following the proposed optimal process shift design an increase of the
matching probability of about 95% is met, towards the case where no adaptation is
98
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
3-shifts [Kannan and
Jayabalan [2002]]
(b∗, p∗ )=(0.139,0.286)
3-shifts [Matsuura and
Shinozaki [2011b]]
(b∗, p∗ )=(0.171,0.35)
5-shifts proposed
optimal design
(b∗1, b∗2, p
∗1, p
∗1 )=
(0.133,0.262,
0.225,0.022)
Bin n◦ X Y Ri X Y Ri X Y Ri
0.001 0.000 0.001 0.000 0.001 0.001
1 0.011 0.002 0.002 0.011 0.002 0.0023 0.011 0.011 0.011
2 0.055 0.066 0.055 0.055 0.063 0.0546 0.055 0.055 0.055
3 0.160 0.192 0.160 0.160 0.160 0.1598 0.160 0.160 0.160
4 0.273 0.240 0.240 0.273 0.274 0.2734 0.273 0.273 0.273
5 0.273 0.240 0.240 0.273 0.274 0.2734 0.273 0.273 0.273
6 0.160 0.192 0.160 0.160 0.160 0.1598 0.160 0.160 0.160
7 0.055 0.066 0.055 0.055 0.063 0.0546 0.055 0.055 0.055
8 0.011 0.002 0.002 0.011 0.002 0.0023 0.011 0.011 0.011
0.001 0.000 0.001 0.000 0.001 0.001
Matching 0.912 0.980 0.997
Surplus 0.085 0.017 0.003
Table 5.6: Details results in the application of three alternative methods for Case 1.
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5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Figure 5.8: Matching probability as a function of the number of shifts - Case 2.
applied. Therefore, the benefits of the proposed approach increase when the process
that is shifted is more capable. Table 5.9 illustrates the specific results of the methods
proposed by Matsuura and Shinozaki [2011b], Kannan and Jayabalan [2002] and the
optimal shift design proposed, for Case 2.
Iteration Shift Matching Probability
1 1 49.68%
2 3 93.57%
3 5 99.33%
4 7 99.73%
5 9 99.73%
Table 5.7: Maximum matching probability for a given number of shifts in Case 2.
5.1.3 The Effect of Optimal Process Adaptation on the System Per-
formance Applying Simulation Model
In order to analyze the impact of the developed process adaptation design method on
the integrated quality and logistics performance of the overall selective and adaptive
assembly systems a discrete event simulation model was developed. This simulation
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5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Bin number
Partitioning Probabilities
X YX Y Ri
Min Max Min Max
2.30 2.05 0.0014 0 0
1 2.30 2.39 2.05 2.14 0.0068 0.000 0.000
2 2.39 2.48 2.14 2.23 0.027 0.000 0.000
3 2.48 2.57 2.23 2.32 0.079 0.000 0.000
4 2.57 2.66 2.32 2.41 0.1598 0.02 0.02
5 2.66 2.75 2.41 2.50 0.2257 0.48 0.23
6 2.75 2.84 2.50 2.59 0.2257 0.48 0.23
7 2.84 2.93 2.59 2.68 0.1591 0.02 0.02
8 2.93 3.02 2.68 2.77 0.0790 0.000 0.000
9 3.02 3.11 2.77 2.86 0.0277 0.000 0.000
10 3.11 3.20 2.86 2.95 0.0068 0.000 0.000
3.20 2.95 0.0014 0.000 0.000
Matching 0.5
Surplus 0.5
Table 5.8: Binning and probabilities for Case 2, without process adaptation.
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5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
3-shifts [Kannan and
Jayabalan [2002]]
(b∗, p∗ )=(0.171,0.35)
3-shifts [Matsuura and
Shinozaki [2011b]]
(b∗, p∗)=(0.17,0.27)
5-shifts proposed
optimal design
(b∗1, b∗2, p
∗1, p
∗1 )=
(0.156,0.304,
0.2365,0.044 )
Bin n◦ X Y Ri X Y Ri X Y Ri
0.001 0.000 0.001 0.000 0.001 0.000
1 0.007 0.000 0.000 0.007 0.000 0.000 0.007 0.005 0.005
2 0.027 0.004 0.005 0.027 0.004 0.004 0.027 0.031 0.028
3 0.079 0.142 0.079 0.079 0.111 0.079 0.079 0.078 0.079
4 0.160 0.196 0.159 0.160 0.159 0.159 0.160 0.159 0.159
5 0.226 0.156 0.156 0.226 0.226 0.226 0.226 0.226 0.226
6 0.226 0.156 0.156 0.226 0.226 0.226 0.226 0.226 0.226
7 0.159 0.196 0.159 0.159 0.159 0.159 0.159 0.159 0.159
8 0.079 0.142 0.079 0.079 0.111 0.079 0.079 0.078 0.079
9 0.028 0.004 0.005 0.028 0.004 0.004 0.028 0.031 0.028
10 0.007 0.000 0.000 0.007 0.000 0.000 0.007 0.005 0.005
0.001 0.000 0.001 0.000 0.001 0.000
Matching 0.798 0.936 0.993
Surplus 0.202 0.064 0.007
Table 5.9: Details results in the application of three alternative methods for Case 2.
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5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Figure 5.9: Schematic representation of selective and adaptive assembly systems for the
experiments.
model includes realistic assumptions on the overall system behavior that are summa-
rized in the next section.
Simulation Model Assumptions. Selective and adaptive assembly systems where
sub-assemblies X and Y are assembled are considered. The system layout is repre-
sented in Figure 5.9, where machining and assembly stations are represented as light
blue squares, inspection stations are represented as red squares and buffers are repre-
sented as yellow circles.
The components X and Y are respectively processed by machines Mx and My. They
are considered to be unreliable and subject to failures. For machine Mx (My) the prob-
ability of failure is px = 1/MTTFx(py = 1/MTTFy) and the probability of repair is
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5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
rx = 1/MTTRx(ry = 1/MTTRy). It is assumed that there is always available material
upstream Mx and My, i.e. they are never starved.
After the process, each component is inspected and sorted into the downstream bins
according to the measured dimensional key characteristic. In line with the previously
introduced assumptions, a total number of n quality classes are defined for both X and
Y, namely Bxi and By
i , with i = 1, ., n. The capacity of each buffer is finite and equal
to Nxi and Ny
i , which are natural numbers.
The assembly station MA, takes one sub-assembly X and one of sub-assembly Y from
the corresponding bins and assemble them. Matching process is assumed as one by
one matching between buffers of sub-assembly X and Y. In other words, the assembly
machine Ma can assemble sub-assemblies X in buffer Bxi only with sub-assemblies Y in
Byi , with i = 1, , n. The assembly station is also assumed to be unreliable and subject
to failures. In details, MA fails with probability Pa = 1/MTTFa and is repaired with
probability ra = 1/MTTRa.
The material flow dynamics is modeled by a discrete flow of parts. Each machine has
the same processing time, scaled to the time unit. If operational, a machine starts
processing one part at the beginning of the time unit. The buffer levels are updated
at the end of the time unit. Inspection stations are assumed to take negligible time to
measure the components.
In order to avoid the deadlock state, in this model we select the discard policy. Accord-
ing to the discard policy , whenever a sub-assembly is produced, either at machine Mx
or My and the buffer where it should be placed is full, the component is discarded. As
mentioned earlier, although this strategy entails a loss of system total throughput, it
allows avoiding deadlock states.
Simulation Results. The optimal shifts designs obtained for the two previously
analyzed experiments have been tested at system level with the simulation model.
In addition to the data reported in Table 5.3, failure probabilities have been set to
px = 0.034, rx = 0.43, py = 0.034, ry = 0.43, pa = 0.033, ra = 0.33. As a consequence,
104
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
the assembly station results to be the bottleneck machine in the system, with an iso-
lated efficiency of 0.9 (both Mx and My have efficiency equal to 0.924). All buffer sizes
are set to 40. The experiments were run for 20 replicates of approximately 18,000 time
units of operation. Table 5.10 shows the simulation results for Case 1. 95% confidence
interval widths are 0.01% and 4% of the average throughput and the WIP, respectively.
Shift ETot. WIP
1 0.58 305.11
3∗ 0.84 269.26
3 0.89 203.97
5 0.90 127.71
Table 5.10: Case 1: Simulated total throughput and WIP for different shifts designs (3*
denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).
For Case 1, the proposed optimal 5-shifts design improved the total throughput of the
system by 53%, 6%, and 1% compared to no-shift design, 3-shifts design proposed by
Kannan and Jayabalan [2002], and 3-shifts design proposed by Matsuura and Shinozaki
[2011b], respectively. It also significantly reduced WIP, by approximately 58%, 53%,
and 37% comparing to no-shift design, 3-shifts proposed by Kannan and Jayabalan
[2002] and 3-shifts proposed by Matsuura and Shinozaki [2011b], respectively. Figure
5.13 and 5.11 show the observed throughput and WIP.
Table 5.11 shows the simulation results for throughput and WIP applying different
shifts designs for Case 2. The optimal 5-shifts design improved throughput of the sys-
tem by 92%, 20%, and 5.9% compared to no-shift design, the 3-shifts design proposed
by Kannan and Jayabalan [2002], and the 3-shifts design proposed by Matsuura and
Shinozaki [2011b]. The WIP is reduced by 47%, 43% and 34% compared to no-shift
design, to the 3-shifts design proposed by Kannan and Jayabalan [2002], and to the
3-shifts design proposed by Matsuura and Shinozaki [2011b]. Figure 5.13 and 5.13 show
the optimal design improvements on system throughput and WIP, respectively.
As shown by this set of results, by adapting the process target with the proposed ap-
proach the throughput of the system can be improved by simultaneously reducing the
105
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Figure 5.10: Observed throughput under different shifts designs for case 1.
Figure 5.11: Observed WIP under different shifts designs for case 1.
106
5.1. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMSDEFINITION
Figure 5.12: Observed throughput under different shifts designs for case 2.
Figure 5.13: Observed WIP under different shifts designs for case 2.
107
5. SELECTIVE AND ADAPTIVE ASSEMBLY SYSTEMS
Shift ETot. WIP
1 0.4638 378.4
3∗ 0.7399 355.4
3 0.8427 305.8
5 0.8928 200.7
Table 5.11: Case 2: Simulated total throughput and WIP for different shifts designs (3*
denotes the 3-shifts design proposed by Kannan and Jayabalan [2002]).
work in progress of the system and meeting high product quality standards. The results
of this analysis is published in Colledani and Ebrahimi [2012].
In particular, we showed that the proposed method to derive the optimal number of
process shifts outperforms existing techniques. Results show that process adaptation
may help to increase the matching probability in the system and, consequently, to
increase the system production rate and to decrease the system WIP, while meeting
desired product quality targets.
In this chapter we have analyzed and explore the behavior of the selective and adaptive
assembly systems. In particular, we have applied the process adaptation in the manu-
facturing process in order to reduce the discard rate of sub-assemblies. The proposed
method is modeled within the analytical performance measurement framework of the
selective assembly systems which is addressed in previous chapters. Moreover, the pro-
posed optimal process adaptation design is addressed. Finally, we illustrate the effect
of process adaptation in system level performance of selective and adaptive assembly
systems. We have shown that the optimal process adaptation design can considerably
reduces the WIP while increases the throughput of the system. Although the process
adaptations are significantly beneficial to increase the efficiency of the selective assem-
bly systems, but not all the manufacturing processes are able to produce with several
mean target values. Therefore, we proposed new intelligent flow control policies to
handle better the logistic complexity of the selective assembly systems. In the next
chapter we explore the proposed policies and their effect on the deadlock state and the
consequent discard rate.
108
6
Deadlock State Correction
Policies
In order to manage the deadlock states, we proposed 5 new flow control policies. These
innovative policies are based on the observable state of the system. The proposed
policies are embedded within our simulation model and the effects of each policy on
system level performance is explored analyzed. There are two different type of policies:
Assembly level policies and Sub-assembly manufacturing level policies. In the following
section we describe the policies in details and then we will discuss about the selective
assembly system behavior under the proposed policies in the next section.
6.1 Assembly Level Policies
Reactive Class Mixing. When the selective assembly system is in deadlock state,
the assembly machine is starved because there are no coupled non-empty buffers to
select for assembly operation. At the same time, both sub-assembly manufacturing
machines are blocked due to a single full buffer. In reactive class mixing of assembly
level policies, we proposed to rule the assembly machine to mix the sub-assemblies
of uncoupled buffers which are non-empty. In the other words, when the assembly
machine is starved while there are unmatched sub-assemblies, the assembly machine
selects the available sub-assemblies although they do not belong to the same quality
class. Figure 6.1 depicts graphically this policy. The black circles depicts the full buffer
while the white circle shows the empty buffer.
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6. DEADLOCK STATE CORRECTION POLICIES
Figure 6.1: Assembly Level Policies: Reactive Class Mix.
It must be notice that, the manufacturing machines are blocked when only one buffer
is full following the blocking before service assumption. Thus the system generates no
discarded sub-assemblies. In fact, the benefit of zero discard rate is paid by the cost
of mixed class assemblies and the consequent decreased system yield level. These kind
of assemblies (the mixed quality class), still can be conforming however it depends on
the partitioning policy and the key characteristic distribution of sub-assemblies.
Preventive Class Mixing. As it can be realized from the name of this policy, the
assembly machine prevents the deadlock state through mixing the unmatched quality
classes prior to the deadlock state. This is because the deadlock state is reached from
the particular states in which the assembly machine is starved. This is the reason that
we minimize the starvation probability of assembly machine in this policy. In order
to do so, the assembly machine is permitted to mix the uncoupled classes whenever
it is starved, regardless of the manufacturing machine states. The manufacturing ma-
chines are blocked when only a single buffer is full, therefore there is no discarded
sub-assemblies. This policy is depicted in Figure 6.2 where the gray circles shows non-
empty and not full buffers.
110
6.1. ASSEMBLY LEVEL POLICIES
Figure 6.2: Assembly level policies: Preventive Class Mix.
Similar to the Reactive Class Mixing policy, the benefit of zero discard sub-assemblies
are paid by the mixing of the quality classes. The main difference to the Reactive Class
Mixing is the fact that in Preventive Class Mixing, the assembly machine mixes the
quality classes much more frequent. This is because the assembly machines mixes the
quality classes whenever it is starved and does not wait for the deadlock state to occur.
The system yield is expected to be reduced comparing to the Reactive Class Mixing,
while the total throughput is expected to be increased.
Buffer Level Dependent. In general, the final assembled product in selective as-
sembly system have the same essence. This means there are no specific preference
within the assembled part of first quality classes or the second quality classes. There-
fore, in this policy the assembly machine is permitted to select the coupled buffers in
such a way that the blocking probability for the manufacturing machines are reduced,
following the algorithm represented in 1.
It must be notice that the manufacturing machines follow the discard rule (as shown
in figure 6.3)because the Buffer Level Dependent policy cannot be applied to avoid the
deadlock state. This policy is proposed to reduce the discard rate. Applying this policy
results in the same system yield as the discard rule because the quality classes are not
mixed by the assembly machine. Meanwhile, the discard rate is expected to be reduced
because the assembly machine reacts smart to the system state in terms of buffer levels.
The assembly machine selects the coupled buffers that is more probable to be full. In
111
6. DEADLOCK STATE CORRECTION POLICIES
Algorithm 1: Buffer Level Dependent
if Max{BX1levelBX1Size
, BY1levelBY1Size
}>Max
{BX2level/BX2SizeBY2level/BY2Size
}then
Select the x1 and y1 matches;
else if Max{BX1levelBX1Size
, BY1levelBY1Size
}<Max
{BX2level/BX2SizeBY2level/BY2Size
}then
Select the x2 and y2 matches;
else
go to αa strategy;
end
Figure 6.3: Assembly Level Policy: Buffer Level Dependent.
this way it reduces the probability of blocking of the manufacturing machines. This
leads to reduced discard rate.
6.2 Sub-assembly Manufacturing Level Policies
The second type of the deadlock correction policies are concern with the sub-assemblies
manufacturing level. In these set of policies, the assembly machine remains with the
same policy as the original selective assembly system, it means the selection of the
sub-assemblies is based on matching sub-assemblies from the coupled buffers . Thus,
these set of policies are imposed only on the manufacturing machines. The proposed
policies are introduced to improve the system level performance of selective assembly
systems in terms of the discard rate reduction.
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6.2. SUB-ASSEMBLY MANUFACTURING LEVEL POLICIES
Figure 6.4: Manufacturing machine level policies: System Level Discard.
System Level Discard Policy. By following the traditional discard policy the sys-
tem state is neglected when the sub-assemblies are discarded. In the other words, the
discard policy is imposed to the manufacturing machines regardless of the system state.
The traditional discard policy permits the manufacturing machines to process a sub-
assembly whenever there is a full buffer downstream. If the processed sub-assembly
has to be placed in the full buffer the machine discards it. In fact, the manufacturing
machines discard the sub-assemblies in states which are not deadlock state in addition
to the deadlock states. For example, considering the selective assembly system with two
classes, if the assembly machine is not starved, thus the system is not in deadlock state,
and one of the buffers of manufacturing machines is full, the manufacturing machine
might discard the sub-assemblies due to the discard policy. However in our proposed
policy, System Level Discard Policy, the manufacturing machines are allowed to follow
the discard rule only if the system is in deadlock state. In the other words, the discard
policy is applied by considering the system state and not only the manufacturing ma-
chines’ state. The schematic view of the system level discard policy is shown in Figure
6.4. Again, the black circles indicate the full buffers and the white circles represent the
empty buffer.
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6. DEADLOCK STATE CORRECTION POLICIES
Figure 6.5: Manufacturing machine level policies : System Level Discard 1 Machine.
System Level Discard Policy Single Machine. In some assemblies one of the
sub-assemblies is much more expensive comparing to the other one. Therefore, it
is not economical to discard both of them even with the proposed reduced discard
rate. Therefore, we proposed to impose the system level discard rule for only the
manufacturing machine that processes the cheaper sub-assembly. In the other words,
the selective assembly system continue the production until it goes to deadlock state
and then only one of the manufacturing machines follow the discard rule. Figure 6.5
represents the System Level Discard Policy Single Machine.
6.3 Numerical results of the deadlock correction policies
As mentioned before, the proposed policies are implemented in the simulation mod-
els. We have tested the proposed policies for 6 different set of experiments to observe
the system level performance measures. In these experiments we have assumed the
assembly of two sub-assemblies, namely X and Y. Sub-assemblies key characteristics
are distributed normally. Each sub-assembly is classified in two quality classes. The
final assembled product key characteristics is identified as the clearance between two
sub-assemblies, namely X−Y . The machines are unreliable and buffer sizes are limited
(fixed to 10 for each buffer).
114
6.3. NUMERICAL RESULTS OF THE DEADLOCK CORRECTIONPOLICIES
Due to the fact that the proposed policies effects depend on the sub-assemblies key
characteristic distribution and the final assembly tolerance limits, we have design the
experiments by considering the machine and buffer parameters as fixed numbers. The
parameters that we have considered as variables are σx, the process variation of the
sub-assembly X and τ as the tolerance of the clearance between the two sub-assemblies
key characteristics (X − Y ). For σx we considered two levels while for the clearance
tolerance we have considered three levels. Levels of σx are considered as 0.06 and 0.12,
that is σx/σy = 1.2 and σx/σy = 2.4, respectively.
6.3.1 Experiments
Table 6.1 shows the considered parameters of all the experiments. For each experiment
we run the simulation model for 10 replications of 900000 time unit, 100000 time unit
is considered for warm-up period. The detail results of each experiment including the
confidence intervals are provided in Tables 6.2, 6.3, 6.4, 6.5, 6.6 and 6.7.
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Experimental Plan
X Y Z
X (µx, σ2x) Y (µy, σ
2y) Z (µx − µy, σ2y + σ2x)
1
µx=4 σx=0.06 µy = 3.3 σy=0.05 µz=0.7 σz=0.0781
1 LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.65 USLz = 0.75
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
2
µx=4 σx=0.06 µy=3.3 σy=0.05 µz=0.7 σz=0.0781
LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.6 USLz = 0.8
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
3
µx=4 σx = 0.06 µy=3.3 σy=0.05 µz=0.7 σz=0.0781
3 LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.5 USLz = 0.9
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
4
µx=4 σx=0.12 µy=3.3 σy=0.05 µz=0.7 σz=0.0781
LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.65 USLz = 0.75
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
5
µx = 4 σx = 0.12 µy=3.3 σy = 0.05 µz=0.7 σz=0.0781
5 LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.6 USLz = 0.8
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
6
µx = 4 σx = 0.12 µy=3.3 σy = 0.05 µz=0.7 σz=0.0781
LSLx = 3.82 USLx = 4.18 LSLy = 3.15 USLy = 3.45 LSLz = 0.5 USLz = 0.9
px = 0.01rx = 0.05 py = 0.01ry = 0.05 pa = 0.01ra = 0.05
Table 6.1: Experimental plan for deadlock correction policies.
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Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,44311 0,00178 0,71076 0,00089728 0 0
Preventive Mix 0,67835 0,00434 0,47133 0,00247 0,69481 0,00093557 0 0
Sys. Level discard 2M 0,59318 0,00506 0,42982 0,00359 0,72462 0,00094771 0,03055 0,00010003
Sys. Level discard 1 M 0,66013 0,00125 0,47852 0,00119 0,72488 0,00065202 0,07835 0,00097728
Process Adaptation 0,68223 0,00258 0,48817 0,0022 0,71555 0,00108 0,10443 0,00053053
B.L. Dependent 0,6799 0,0031 0,49253 0,00196 0,72442 0,00102 0,12427 0,00037229
Discard 0,67547 0,00306 0,48932 0,00191 0,72441 0,00122 0,14252 0,00071429
Table 6.2: Performance measures results for experiment 1.
Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,59115 0,00272 0,9482 0,00048582 0 0
Preventive Mix 0,67835 0,00434 0,63601 0,00407 0,93757 0,00026045 0 0
Sys. Level discard 2M 0,59318 0,00506 0,56746 0,00463 0,95666 0,00051991 0,03055 0,000866
Sys. Level discard 1 M 0,66013 0,00125 0,63157 0,000978 0,95672 0,00040282 0,07835 0,001840
Process Adaptation 0,68223 0,00258 0,65075 0,00242 0,95385 0,00038117 0,10443 0,000206
B.L. Dependent 0,6799 0,0031 0,65037 0,00285 0,95657 0,00038136 0,12427 0,003121
Discard 0,67547 0,00306 0,64611 0,0027 0,95653 0,00033372 0,14252 0,004255
Table 6.3: Performance measures results for experiment 2.
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Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,62297 0,00309 0,99924 0,000038355 0 0
Preventive Mix 0,67835 0,00434 0,67739 0,00431 0,99857 0,000054014 0 0
Sys. Level discard 2M 0,59318 0,00506 0,59305 0,00506 0,9998 0,000033082 0,03055 0,00086668
Sys. Level discard 1 M 0,66013 0,00125 0,66001 0,00124 0,9998 0,00001229 0,07835 0,00184064
Process Adaptation 0,68223 0,00258 0,68209 0,00257 0,999794791 0,00001229 0,10443 0,00020679
B.L. Dependent 0,6799 0,0031 0,67975 0,00309 0,99979 0,000030846 0,12427 0,00312182
Discard 0,67547 0,00306 0,67533 0,00306 0,9998 0,000012932 0,14252 0,00425528
Table 6.4: Performance measures results for experiment 3.
Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,29201 0,00153 0,46839 0,0011 0 0
Preventive Mix 0,67835 0,00434 0,30936 0,00245 0,45604 0,00097963 0 0
Sys. Level discard 2M 0,59318 0,00506 0,28388 0,00295 0,47858 0,00106 0,03055 0,00086668
Sys. Level discard 1 M 0,66013 0,00125 0,31598 0,00104 0,47865 0,00093863 0,07835 0,00184064
Process Adaptation 0,68223 0,00258 0,32712 0,00167 0,47948 0,00144 0,10443 0,00020679
B.L. Dependent 0,6799 0,0031 0,32491 0,00173 0,47788 0,00113 0,12427 0,00312182
Discard 0,67547 0,00306 0,32272 0,00191 0,47778 0,00112 0,14252 0,00425528
Table 6.5: Performance measures results for experiment 4.
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Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,453 0,00204 0,72662 0,00044662 0 0
Preventive Mix 0,67835 0,00434 0,48462 0,00322 0,7144 0,00029744 0 0
Sys. Level discard 2M 0,59318 0,00506 0,4373 0,00389 0,73723 0,00047895 0,03055 0,00086668
Sys. Level discard 1 M 0,66013 0,00125 0,4864 0,0012 0,73682 0,000577 0,07835 0,00184064
Process Adaptation 0,68223 0,00258 0,50613 0,00206 0,74187 0,00094644 0,10443 0,00020679
B.L. Dependent 0,6799 0,0031 0,50083 0,00225 0,73663 0,00080086 0,12427 0,00312182
Discard 0,67547 0,00306 0,49739 0,0024 0,73637 0,00094956 0,14252 0,00425528
Table 6.6: Performance measures results for experiment 5.
Policy TH Tot. CI TH Eff CI System Yield CI Discard Rate CI
Reactive Mix 0,62345 0,0031 0,58883 0,00288 0,94447 0,00044606 0 0
Preventive Mix 0,67835 0,00434 0,63732 0,0041 0,93949 0,00015416 0 0
Sys. Level discard 2M 0,59318 0,00506 0,56253 0,00454 0,94834 0,00057735 0,03055 0,00086668
Sys. Level discard 1 M 0,66013 0,00125 0,62595 0,00111 0,94822 0,00032379 0,07835 0,00184064
Process Adaptation 0,68223 0,00258 0,64822 0,00247 0,95014 0,00038158 0,10443 0,00020679
B.L. Dependent 0,6799 0,0031 0,64469 0,00296 0,94821 0,00039811 0,12427 0,00312182
Discard 0,67547 0,00306 0,6406 0,00267 0,94838 0,00056311 0,14252 0,00425528
Table 6.7: Performance measures results for experiment 6.
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6. DEADLOCK STATE CORRECTION POLICIES
Figure 6.6, 6.7, 6.8, 6.9, 6.10 and 6.11 graphically illustrate the effect of proposed
policies on the effective throughput for experiment 1 to 6, respectively. Althought in
most cases our proposed process adaptation policy, which is introduced in chapter
“Selective and Adaptive Assembly Systems”, is out-performing our other flow control
policies in terms of the effective throughput, but the main aim to introduce these new
flow control policies was to reduce the discard rate. The effect of proposed flow control
policies on the discard rate of the system is illustrated in Figure 6.6, 6.7, 6.8, 6.9, 6.10
and 6.11 for experiments 1 to 6, respectively.
For instance, consider the experiment number 4; although in Reactive Mix policy and
Preventive Mix policy the effective throughput is reduced by 9.5% and 4.1%, respec-
tively, comparing to the discard policy, the discard rate is reduced to zero from 0.142
parts per time unit. This is because the manufacturing machines are blocked when
one buffer become full, thus they discard no sub-assemblies while the deadlock state is
avoided. For System level discard 2M, System level discard 1M, Process Adaptation
and Buffer Level dependent policies, the discard rate is reduced by 78.56%, 45.0252%,
26.7260% and 12.8052%, respectively.
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Figure 6.6: Experiment1: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.7: Experiment2: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.8: Experiment3: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.9: Experiment4: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.10: Experiment5: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.11: Experiment6: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.12: Experiment1: The discard rate for proposed deadlock correction policies.
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Figure 6.13: Experiment2: The discard rate for proposed deadlock correction policies .
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Figure 6.14: Experiment3: The discard rate for proposed deadlock correction policies.
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Figure 6.15: Experiment4: The discard rate for proposed deadlock correction policies.
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Figure 6.16: Experiment5: Effective throughput behavior for proposed deadlock correction policies.
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Figure 6.17: Experiment6: The discard rate for proposed deadlock correction policies.
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6.3. NUMERICAL RESULTS OF THE DEADLOCK CORRECTIONPOLICIES
From the discard reduction point of view, considering the Figures of the discard policy
(Figure 6.12, 6.13, 6.14, 6.15, 6.16 and 6.17), we can conclude that the proposed policies
are all out-performing the Discard Policy which is proposed in the literature. As it can
be noticed from the results, the Preventive Class Mixing and Reactive Class Mixing
policies reduce the discard rate to zero. Taking into account the 6 set of experiments
we can prioritize the policies based on the effect on the discard rate, as following:
1. Reactive Mix
2. Preventive Mix
3. System level discard 2M
4. System level discard 1M
5. Process Adaptation
6. Buffer Level dependent
7. Discard
It must be noticed that this prioritization is not valid if the comparison is carried out
based on the effective throughput.
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7
Selective Assembly Application
in Electrical Engine Production:
Bosch Case
7.1 Introduction
Only limited number of case studies have been analyzed in the literature of manufac-
turing system analysis, although the considerable effort devoted to this research field.
Their aim was mainly to provide practical validation of the analytical models, rather
than supporting the company in the challenging issue of constantly increasing the pro-
ductivity of its manufacturing operations. Therefore, there are only few collaboration
projects between industry and academy where the analytical performance evaluation
tools are applied for system performance estimation and improvement.
Colledani et al. [2010] reported the results of a collaboration project between Politec-
nico di Milano (Milano, Italy), Kungliga Tekniska hogskolan (Stockholm, Sweden) and
Scania CV AB (Sodertalje, Sweden) in the area of manufacturing system productivity
improvement. In this project a high increment in throughput and considerable savings
in work-in-progress (WIP) is achieved in the six-cylinder engine-block manufacturing
system. The project also provided company with an integrated and formalized method-
ology for manufacturing system configuration, reconfiguration and continuous improve-
ment. Freiheit et al. [2007] explore the operational cost differences between high-volume
135
7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
serial CNC-based manufacturing systems and parallel CNC-based manufacturing sys-
tems. In Alden et al. [2006] approaches and the results achieved by General Motors
Corporation in a long-term project to evaluate and increase the throughput performance
of its production lines is reported. Patchong et al. [2003] addressed the improvement
method of the car body production at PSA Peugeot Citroen, where an iterative three-
step design method was developed to improve the system throughput. The method
includes both analytical and simulation models. The proposed method improved the
throughput with the minimal capital investment and no compromise in terms of quality.
Liberopoulos and P.Tsarouhas [2002] collaborate in a project to determine cost-efficient
methods of speeding up the croissant processing lines of Chipita International Inc., one
of the largest Greek manufacturers of bakery products and snacks. They have shown
that the proper buffer allocation at a specific point of the line led to a reduction in
failure impact and an increase of the system performance efficiency. Almgren [2000]
considered the experience of Volvo Car Corporation. The author examined the pilot
production and the manufacturing process start-up of the Volvo S80 model. The main
aim of this case study was to contribute to the understanding of the way the ramp-up
process was affected by certain types of disturbances. Burman et al. [1998] studied
on the application of analytical methods to design a system for manufacturing ink-
jet printers at Hewlett-Packard Corporation. Great benefits for the company through
assigning of more buffer space in the manufacturing line supported by the use of ap-
proximate analytical techniques is provided. In this chapter we describe the application
and benefits of implementing selective assembly systems in production of the electrical
engines in Bosch company. The results of the proposed approaches are published as
deliverable of EU funded project (MuProD [2013d]), MuProD “Innovative proactive
Quality control system for in-process multi-stage defect reduction”.
7.2 Bosch Electrical Engine manufacturing system descrip-
tion
The manufacturing system of the Bosch plant producing electrical engines for the e-
mobility sector in Hildesheim is considered for this case study. The electrical engines
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7.2. BOSCH ELECTRICAL ENGINE MANUFACTURING SYSTEMDESCRIPTION
Figure 7.1: Integrated Mototr Generator (Bosch).
are Integrated Motor Generator (IMG), permanent magnet excited synchronous ma-
chine with an inner rotor, as shown in Figure 7.1. The rotor of the IMG consists of a
cylindrical rotor carrier and laminated steel stacks. Each steel stack is provided with
interior mounted permanent magnets. Those magnetic steel stacks are assembled to
the rotor carrier through defined interlocking angle.
A modeled schema of this plant is represented in Figure 7.2. The system is composed
of two main branches, respectively dedicated to the assembly and magnetization of the
rotor and to the stator production. The assembly of these two sub-assemblies takes
place at a downstream assembly stage and the complete engine is produced. The as-
sembly key characteristics of the engine is the magnetic moment which is measured and
if it is observed to deviate more than 4% from its target value, the product is identified
as a defect to be scrapped.
The quality control of the engines currently takes place at the end of the line (EOL test-
ing), similar to the most of multi-stage production systems. The main disadvantage of
EOL inspection is the off-line inspection at the final stage of the manufacturing system,
where already all defects of the production system have been generated. Therefore, the
EOL testing prevents from any possible repair operation. To overcome this drawback
it is necessary to create solutions to reduce either defect generation or defect propaga-
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.2: Schema of Current Manufacturing System.
tion. In this case study we focus on reducing the final assembly defect generation by
adapting the selective assembly system in the assembly station of the production line
of electrical engines.
7.2.1 Manufacturing Stages
The main focus of the analysis is on the rotor assembly. In details the system is
composed of seven main stages, dedicated to the following operations:
• M1: loading of the stacks on the pallet.
• M2,1,M2,2: two parallel stations assembling the magnets on the stacks. The sta-
tions are composed of a pick and place system for the positioning of the magnets
in their locations. Moreover, the glue is dispensed at the interfaces between the
magnets and the stacks surface. Finally, the glue is thermally treated in a single
oven for both parallel stages.
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7.2. BOSCH ELECTRICAL ENGINE MANUFACTURING SYSTEMDESCRIPTION
• M3: Stack magnetization process. Each stack is centered in the magnetization
device that is produced by a supplier and currently un-controlled by Bosch. As
a matter of fact, it is treated as a black box. It is known that it works in the
saturation regime.
• M4: heating station. A rotating table carrying 4 magnetized stacks moves the
stack into a heating chamber for preparing the stack to the next assembly oper-
ation. Indeed the assembly principle is based on mechanical interference. Since
it has 4 stacks position, it could be used in the future as a sequence decoupling
stage.
• M5: assembly machine. The required number of stacks, normally varying from
5 to 10 for different product types, is taken from the heating machine and a pile
of stacks in the z axis of the machine is formed by mounting each stack on the
central shaft. This represents the core of the rotor. In the current production
line, the angle between the rotor stacks is fixed and cannot be changed by the
operators.
• M6: rotor balancing station.
• M7: rotor marking station.
The remaining stations perform the following operations:
• Mx,Mz,Mk,Mj : processes of stator assembly, not treated in detail in this case
study.
• Mg: assembling rotor and stator together.
• Mk: End-of-line (EOL) testing of final motor where several motor properties are
measured.
A new measurement devices are included at stages M3 and M5 for detection of devia-
tions in the magnetic field of a single rotor stack and the complete rotor, respectively
(MuProD [2013a,b]). In details, these actions include:
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
• The development of a new sensor for the space resolved measurement of the
magnetic field of each single stack. This will result in an additional inspection
point that will be located after machine M3.
• The development of a new multi-sensor system distributed in the z axis of the
rotor, for measuring the field of each stack in the assembled rotor and check for
uniformity of the overall rotor field after stage M5.
7.2.2 Modeling Approach
The main modeling assumptions which are applied for performance evaluation model
are summarized below:
1. Since buffers B1.1 and B1.2 are provided with the same stacks from the upstream
machine M1, they are considered as a single buffer transferring the stacks to both down-
stream machines.
2. According to the current configuration of Bosch production line, both machines M2.1
and M2.2 are performing the same operation, assembling the magnets on the stacks.
Therefore they are considered as two parallel machines in the model.
3. Parallel machines M2.1 and M2.2 are fed by two out-of-line buffers, B0.1 and B0.2, in
which magnets raw part are stored. The capacity of those buffers is considered infinite
and therefore the magnets raw parts are always available.
4. Buffer B4 behaves a bit different compared to other buffers of the line. Since 5
magnetized stacks are required to be assembled in the downstream machine M5, the
buffer B4 is required to have the availability at least of 5 magnetized stacks.
5. Having assembled the rotor at station M5, all the other downstream machines are
aggregated together, since there is no buffer after station M5.
6. The machine M5 is, in theory, an assembly machine. But, since there is no buffer
downstream, the approximation of the assembly operation is provided by considering
the throughput as the number of coupled stacks per minute.
7. The machines Mx, Mz, Mk and Mj , which create the stator assembly line are not
modeled in this case study.
From the available information, it is realized that the system yield is affected by two
machines, i.e. M3 and M5. The schema reported in Figure 7.3, shows the transforma-
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Figure 7.3: Approximation of the original Bosch layout with a multistage process-chain
model.
tion of the original Bosch line model to an approximated equivalent production line.
In order to analytically approximate the performance of the current manufacturing
model, the details about the machines and buffers, as provided by Bosch MuProD
[2013c], are reported in Table 7.1 and Table 7.2 respectively.
Some considerations are provided in the following:
1. M1: The loading of the stacks to the pallets is operated in this machine. It is
subject to a unique operational failure. When the machine is operational, it takes
0.15 minutes to process a stack. Moreover, the machine fails on average every
480 minutes and takes 0.15 minutes to get repaired.
2. B1,2: This buffer is obtained from the coupled buffers B1.1 and B1.2 from the
original model in Figure 7.2. The capacity of the buffer is considered finite and
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Machine MTTF [min] MTTR [min] Cycle time [min] Production unit
M1 480 0.15 0.15 Stack
M2 300 10 1.8 Stack
M3 160 1 0.69 Stack
M4 175200 480 0.667 Stack
M5 28800 150 0.8 Stack
Table 7.1: Mean time to failure, mean time to repair and cycle time of the machines.
Buffer Capacity
B1,2 5
B2,3 40
B3,4 40
B4,5 6
Table 7.2: Capacity of each buffer in the current manufacturing system[number of stacks].
equal to 5.
3. M2: As previously mentioned, machines M2.1 and M2.2 of Figure 7.3 are consid-
ered as parallel machines. Moreover, they are subject to a single failure mode
machines. The processing rate in each machine is 1.8 minutes per stack. About
the reliability, each machine fails on average every 300 minutes and gets repaired
in 10 minutes.
4. M3, M4 and M5 are modeled as single failure mode in the system (data in Table
7.1).
7.2.3 Characterization of the quality parameters
In terms of quality, the problem associated to the spatial magnetization of the rotor
arises from the magnet assembly performed at M2 and the stack magnetization oper-
ations performed at M3 (Colledani et al. [2013]). It gets visible at the new inspection
station designed by Marposs and Bosch and located at M3. Based on prior analysis,
the fraction of stacks featuring non-uniform magnetization is estimated at 6%. There-
fore, considering the generated magnet flux intensity of the coupled stacks as the key
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quality characteristic of the final assembly of rotors, the system yield of the current
manufacturing system, Ysystem, is approximately 94%.
7.3 New Configurations For Rotor Manufacturing Line
The advantage of adopting the selective assembly system is to improve the quality of
the assembled rotor, by compensating the stacks variability. The assembled key quality
characteristic in the following experiments is the sum of the total magnetic flux inten-
sity obtained from coupled stacks. The objective of the selective assembly is to make
this value as close as possible to the target value. In order to obtain the target value,
selective assembly proposes to match the weaker stacks with stronger ones, so that the
variation in the total magnetic flux intensity can be canceled out (the comparison of
normal assembly and selective assembly is provided in Figure 7.4). The system per-
formance of current manufacturing line is then compared with the performance of new
configuration system included selective assembly system. In the following sections the
analysis of the new proposed configurations are provided.
The analyzed configurations to Bosch electrical engine manufacturing includes the se-
lective assembly system with number of quality classes that varies from 2 to 8. In
these particular configurations, number of buffers of the selective assembly cell is equal
to the number of classes, for instance, the selective assembly system of two classes is
connected to two buffers while in the generic selective assembly model, the system of
two classes is identified by four buffers. This is because in this manufacturing system
the final assembly is composed of two similar sub-assemblies that share the same man-
ufacturing machine, while in the generic model each sub-assembly is manufactured in
the dedicated manufacturing machine.
7.3.1 Selective assembly with two quality classes connected to two
buffers.
The selective assembly in this case classifies the measured stacks in two quality classes.
One class is composed of weaker stacks with the sum of the total magnetic flux inten-
sity lower that the target value (39261.6 [Wb]). The second class contains stacks with
stronger magnetization, i.e. with a value of the total magnetic flux intensity greater
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.4: Selective Assembly of stacks: schematic view.
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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE
Figure 7.5: Proposed configuration: Selective assembly system with two classes.
than 39261.6 [Wb]. The assembly machine selects one weaker and one stronger stack in
order to realize a coupled group of two stacks that has a sum of total magnetic fluxes
closer to a target value of 78523.2 [Wb]. The proposed configuration of two quality
classes is depicted in Figure 7.5. This must be noticed that in the proposed configura-
tions including the selective assembly, as the number of quality classes increases, the
total buffer size of the corresponding buffer remains the same as the baseline configu-
ration, which is 40 stacks.
As shown in Figure 7.6 the selective assembly system (blue distribution) was able to
perform better in providing assembled stacks which have lower variability if compared
to the no selective assembly system (red distribution). The corresponding variance us-
ing the selective assembly system of two classes is 6074.1 [Wb2], which implies 63.15%
reduction of variance comparing to 16486.9 [Wb2] which is obtained by normal assembly.
It is worthy to note that the selective assembly can smooth the input variability. The
variance of the single stack total magnetic flux intensity was 8393.37 [Wb] by Monte
Carlo Simulation. The effect of this policy on the output distribution is estimated by
simulating 10,000 stacks, which are used to realize 5,000 assembled stacks. The same
analysis is repeated while assembling according to the order of arrival of the stacks.
This must be noticed that the reduction of variance of generated magnetic flux does not
directly imply the system yield improvement. We will discuss the system performance
improvement in the next section, after introducing each configuration.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.6: Distribution of the magnetic flux intensity of the coupled stacks applying the
selective assembly with two quality classes and normal assembly strategy.
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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE
Figure 7.7: Proposed configuration: Selective assembly system with four classes.
7.3.2 Selective assembly with four quality classes connected to four
buffers.
The selective assembly system in this configuration classifies measured single stacks
into four classes. Each class is connected to one dedicated buffer and the boundaries
of these classed are reported in Table 7.3 (the equal probability partitioning scheme is
considered). The system topology of the proposed configuration is depicted in Figure
7.7.
Equal Probability Scheme For Four Classes
LSL USL
Class 1 38986,17 39199,20999
Class 2 39199,20999 39261
Class 3 39261 39322,79001
Class 4 39322,79001 39535,83
Table 7.3: Equal probability partitioning scheme for four quality classes.
The distribution of total magnetic flux intensity by applying the selective assembly
system of four quality classes (blue distribution in Figure 7.9) features less variability if
compared to the normal assembly strategy, shown in blue. The corresponding variance
with selective assembly is 2734.6 [Wb2]. This is lowered if compared to the value
obtained by using only two classes (6074.1 [Wb2]). It can be noticed that the addition
of two classes lowers the variance of the assembly process by more than a half (54.97%).
The four class selective assembly policy reduces the variance by 84% if compared to
the no-selective assembly policy.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.8: Distribution of the magnetic flux intensity of the coupled stacks applying the
selective assembly with four quality classes and normal assembly strategy.
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Figure 7.9: Distribution of the magnetic flux intensity of the coupled stacks applying the
selective assembly with six quality classes and normal assembly strategy.
7.3.3 Selective assembly with six quality classes connected to six
buffers.
The selective assembly system in this case classifies measured single stacks into six
classes. Each class is connected to a dedicated buffer and the boundaries of these classed
are reported in Table 7.4 (the equal probability partitioning scheme is considered).
The system topology of the proposed configuration is depicted in Figure 7.10. The
variance of the generated magnetic flux intensity in the selective assembly system of
6 quality class is 1345 [Wb2], which is reduced by 103% respecting the no-selective
assembly configuration. The distribution of total magnetic flux intensity by applying
the selective assembly system of four quality classes (blue distribution in Figure 7.9)
features less variability if compared to the normal assembly strategy, shown in blue.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.10: Proposed configuration: Selective assembly system with six classes.
Equal Probability Scheme For Six Classes
LSL USL
Class 1 38986,17 39172,35006
Class 2 39172,35006 39221,54023
Class 3 39221,54023 39261
Class 4 39261 39300,45901
Class 5 39300,45901 39349,62537
Class 6 39349,62537 39535,83
Table 7.4: Equal probability partitioning scheme for six quality classes.
7.3.4 Selective assembly with eight quality classes connected to eight
buffers
The selective assembly in this case classifies the laminated stacks into eight equal prob-
ability partitioned classes. As before, the classes are connected to dedicated buffers as
shown in Figure 7.11. Table ?? shows the equal probability partitions of corresponding
selective assembly with eight quality classes.
The corresponding variance of the assembled stacks from simulated result of selective
assembly of eight quality classes is 1279.1[Wb2], as illustrated in Figure 7.12. The
obtained variance is reduced by 92.25% comparing to the no-selective assembly system.
7.3.5 Comparison of the four analyzed configurations
By comparing the four configurations, it can be observed that the output distribution
(the distribution of the coupled stacks) is getting more centralized to the target value
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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE
Figure 7.11: Proposed configuration: Selective assembly system with eight classes.
Figure 7.12: Distribution of the magnetic flux intensity of the coupled stacks applying
the selective assembly with eight quality classes and normal assembly strategy.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Equal Probability Scheme For Eight Classes
LSL USL
Class 1 38986,17 39155,61649
Class 2 39155,61649 39199,20999
Class 3 39199,20999 39231,80945
Class 4 39231,80945 39261
Class 5 39261 39290,19055
Class 6 39290,19055 39322,79001
Class 7 39322,79001 39366,38351
Class 8 39366,38351 39535,83
Table 7.5: Equal probability partitioning scheme for eight quality classes.
with less variance as the number of quality classes is increased. The reduction of the
assembled stacks variance as the number of quality classes increase is shown in Figure
7.13. However, it should be also noticed that by increasing the number of classes the
complexity of the production logistics increases and higher fraction of surplus, non-
matched, assemblies are generated. In the other words, due to the accumulated surplus
sub-assemblies in the buffers with limited capacities, the manufacturing machines have
to discard with higher rate as the number of classes increases. This results in lower
level of total throughput. Therefore, in order to compare effectively the proposed con-
figurations, these competing effects should be studied under an integrated framework
of quality and production logistic performance. For this reason, we have extend our
simulation model of selective assembly system for more classes, integrated in the corre-
sponding manufacturing system. The simulation model was developed considering the
same assumption as those adopted for developing the approximate analytical method.
Beside, the analytical model can be extended with the same proposed framework as
two quality classes for more quality classes.
The obtained generic performance measures of the proposed selective assembly config-
urations are shown in Table 7.6. This results are obtained by running the simulation
model for 10 replications of 1,000,000 time units for each configuration. Also, 100,000
time unit is considered for the warm-up period. The 95% confidence interval for each
performance measure is provided in the Table 7.6.
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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE
Figure 7.13: Reduction of variance with increasing number of quality classes.
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N. of Classes TH Eff CI TH Tot. CI WIP CI System Yield CIDiscard
rateCI
No Selective
Assembly0,50811 0,003 0,53593 0,002 18,6 1,16 0,94807 0,002 0 0
2 0,51922 0,001 0,52068 0,001 15 1,90 0,99721 0.0004 0,0252 0,002
4 0,51193 0,002 0,51212 0,002 17,4 2,42 0,99962 0.0001 0,04924 0,002
6 0,49868 0,005 0,49876 0,005 14,6 2,85 0,99985 0.009 0,07438 0,005
8 0,48721 0,004 0,48727 0,004 15,4 4,52 0,99989 0.000 0,0947 0,002
Table 7.6: Performance measures of the proposed Selective Assembly configurations.
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7.3. NEW CONFIGURATIONS FOR ROTOR MANUFACTURINGLINE
Consider the total throughput of the system as the number of classes increases, de-
picted in Figure 7.14. As it can be noticed, the total production rate is decreasing as
the number of quality classes increases. This is because as the number of quality classes
increases the complexity of the logistic system increases as well. The complexity of the
logistic system with the finite buffer capacities causes the manufacturing machine blocks
more and due to discard policy, manufacturing machine discards more sub-assemblies
(As it is shown in Figure 7.15). On the other hand, the assembly machine starves more
frequent as the number of quality classes increases due to the lowered level of available
coupled buffers. Therefore, discarding more sub-assemblies in addition to more star-
vation probability of the assembly machine, as the number of quality classes increases,
leads to the reduced total throughput.
Figure 7.14: Throughput total as the number of quality class increases.
Although the total throughput is decreasing, but the system yield is increasing as the
number of quality classes increases, as it is shown in Figure 7.16. Therefore, the conse-
quent effective throughput of the system has a monotone increasingly behavior guided
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.15: Discard Rate as the number of quality class increases.
by the reduced total throughput and the contrasting effect of increased yield, as shown
in Figure 7.17.
As it can be observed in Figure 7.17, the effective throughput behavior differs from
the decreasingly curve representing the total throughput of the system, and it presents
a maximum. This means that there exist an optimal number of quality classes that
maximizes the throughput of the conforming assemblies. This suggests that, according
to the number of quality classes of selective assembly and the resulting quality and
productivity parameters, the system designer should configure the selective assembly
system to reach the maximum of effective throughput curve, without considering the
system yield and total throughput behavior separately. In addition, we showed in Fig-
ure 7.13 that the variance of the generated magnetic flux intensity decreases as the
number of quality classes increase, but by observing the effective throughput we real-
ized that the optimal configuration is the selective assembly system with two quality
classes and considering only the reduced variance of the final assembly key character-
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7.4. THE EFFECT OF FINAL ASSEMBLY KEY CHARACTERISTICTOLERANCE TIGHTENING ON THE EFFECTIVE THROUGHPUT
Figure 7.16: System Yield as the number of quality class increases.
istic obtains the configuration that sub-perform the optimal configuration.
7.4 The Effect of Final Assembly Key Characteristic Tol-
erance Tightening on The Effective Throughput
In order to demonstrate the benefits of the selective assembly comparing to the normal
assembly, we also tested the system performance in the scenario that the requested
tolerance on the final product key characteristic is tightened. This is important be-
cause often tighter tolerances on the final assembly key characteristic leads to the more
performing products. On the other hand, the more tightened tolerance causes the lower
level of the system yield and the effective throughput, while the configuration is fixed.
Therefore, it is needed to jointly consider the effect of quality (tighter tolerance on
the final assembly key characteristic) and the production logistic performance on the
manufacturing system performance under different system configurations.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
Figure 7.17: Effective Throughput as the number of quality class increases.
The manufacturing system characteristics, i.e., the machine reliability data and the
total buffer capacities, are the same as the baseline manufacturing system for both the
normal assembly and the selective assembly systems. Table 7.7 provides the considered
tolerance limits for the experiments.
7.4.1 Experiments Results
In Table 7.8, 7.9 and 7.10, the behavior of the baseline system configuration (no se-
lective assembly) is compared with the proposed selective assembly system with 2, 4,
Tolerance [Wb]
Tol. Std. 503,32
Tol./2 251,66
Tol./4 125,83
Tol./6 83,886
Table 7.7: Tested Tolerance Limits.
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7.4. THE EFFECT OF FINAL ASSEMBLY KEY CHARACTERISTICTOLERANCE TIGHTENING ON THE EFFECTIVE THROUGHPUT
6 and 8 quality classes when the tolerance limit on the key characteristic of the final
assembly (the generated magnetic flux intensity of a coupled stacks) is divided by 2,
4, and 6, respectively. Figure 7.18 represents the effect of the tolerance tightening on
the effective throughput of the baseline manufacturing system as well as the proposed
selective assembly systems.
As it is mentioned earlier, for the case of standard tolerance on the final assembly key
characteristic, denoted as T, the proposed selective assembly with two quality classes
outperform the baseline (no selective assembly) system by 2.18%, while the selective
assembly systems with 4, 6 and 8 quality classes sub-perform the baseline manufacturing
system. However, when the tolerance is tightened to T/2, the 4, 6 and 8 quality class
selective assembly systems improve the effective throughput approximately by 37%,
and the two class selective assembly outperform the baseline manufacturing system by
26.85%. As the tolerance become tighter the positive effect on the effective throughput
become even more visible by the number of quality classes. For instance, T/6 the
effective throughput is improved by 66,1%, 170,6%, 217,8% and 236,7% for 2, 4, 6,
and 8 quality classes, respectively. Therefore, the results highlight the fact that as the
tolerances on the final assembly becomes tighter, selective assembly system with more
quality classes are out-performing more effectively. Even though more quality classes
reduces significantly the total throughput but the contrasting effect of the obtained
yield compensates the effective throughput.
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T/2 TH Tot CI TH Eff CI WIP CI Yield CI Discard Rate CI
No Selective 0,53593 0,002 0,35794 0,003 18,6 7,16 0,66788 0,005 0 0
2 Class 0,51062 0,003 0,45405 0,003 11,4 2,57 0,88923 0,001 0,04888 0,003
4 Class 0,50843 0,001 0,49386 0,002 12,8 3,76 0,97133 0,001 0,0539 0,002
6 Class 0,50456 0,004 0,49761 0,004 15,6 7,58 0,98624 0,001 0,06057 0,006
8 Class 0,50634 0,005 0,50182 0,005 19,8 5,91 0,99106 0,0007 0,05556 0,004
Table 7.8: Performance Measures for the tolerance limit divided by 2 (T/2).
T/4 TH Tot CI TH Eff CI WIP CI Yield CI Discard Rate CI
No Selective 0,53593 0,002 0,19911 0,002 18,6 1,16 0,37152 0,004 0 0
2 Class 0,51062 0,003 0,30917 0,001 11,4 2,57 0,60549 0,004 0,04888 0,003
4 Class 0,50843 0,001 0,43408 0,001 12,8 3,76 0,85376 0,002 0,0539 0,002
6 Class 0,50456 0,004 0,46263 0,004 15,6 1,58 0,91691 0,0009 0,06057 0,006
8 Class 0,50634 0,005 0,47727 0,005 19,8 5,91 0,94257 0,001 0,05556 0,004
Table 7.9: Performance Measures for the tolerance limit divided by 4 (T/4).
T/6 TH Tot CI TH Eff CI WIP CI Yield CI Discard Rate CI
No Selective 0,53593 0,002 0,13569 0,001 18,6 1,16 0,25317 0,002 0 0
2 Class 0,51062 0,003 0,22539 0,002 11,4 2,57 0,44142 0,005 0,04888 0,003
4 Class 0,50843 0,001 0,36727 0,000 12,8 3,76 0,72237 0,003 0,0539 0,002
6 Class 0,50456 0,004 0,43132 0,003 15,6 1,58 0,85485 0,003 0,06057 0,006
8 Class 0,50634 0,005 0,45689 0,005 19,8 5,91 0,90232 0,001 0,05556 0,004
Table 7.10: Performance Measures for the tolerance limit divided by 6 (T/6).
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Figure 7.18: Effect of tightening the tolerance on TH Eff.
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7. SELECTIVE ASSEMBLY APPLICATION IN ELECTRICALENGINE PRODUCTION: BOSCH CASE
162
8
Selective Assembly Application
in Automotive Industry: Door
Assembly in Jaguar and Land
Rover Company
In this section we describe the application of the selective assembly system in auto-
motive industries. As mentioned earlier, selective assembly has been suggested as an
effective approach to support tight dimensional control of part-to-part gap during re-
mote laser welding operations in the automotive industry (FP7-2011-NMP-ICT-FoF
[2012]). In this application, a tight gap control is essential to ensure the high quality of
the produced stitch, in terms of mechanical properties and corrosion resistance. Typi-
cally, the gap cannot be smaller the 0.1[mm] while processing zinc coated sheet metals.
The risk of a smaller gap is the explosion or ejection of molten weld metal caused by
the escape of trapped high pressurized zinc vapor. Moreover, the gap cannot be larger
than 0.3[mm]. The reason is the risk of lack of fusion and insufficient penetration of
the stitch in the components (Steen [1993]). Selective assembly can classify compliant
sheet metals after forming in order to have a homogeneous gap between components
during the welding process, contributing to high quality welding. This requires the
inspection-based characterization of the geometrical variation of the metallic sheets.
The measured data can be characterized by statistical modal analysis (Ceglarek and
Huang [2007]). In this case study, the remote laser welding is proposed to be applied in
163
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
the manufacturing line of door production in Jaguar and Land Rover (JLR) company
instead of the current resistant spot welding technology. The data, results and analysis
of the proposed configurations are reported in deliverable of an EU project, Remote
Laser Welding System Navigator for Eco & Resilient Automotive Factories. In the
following, first we describe the current manufacturing system and the corresponding
manufacturing model, then we will discuss the model of the proposed configuration
which includes the selective assembly system. Finally, we compare the results of the
proposed configuration with that of the current configuration.
8.1 JLR Door Manufacturing System Description
The studied manufacturing system is the assembly line for the front door (left side
and right side) of one of the company’s vehicles. The current manufacturing system
is assembling the door by applying the Resistant Spot Welding, denoted also as RSW.
The material of the sub-assemblies to be welded into a door for a door variant model
is shown in Figure 8.1. Figure 8.2 illustrate the precedence diagram representing the
sub-assemblies precedence for assembly operation through the line. Materials used for
the door assembly are generally, zinc galvanized mild steels and hot formed boron for
the impact beam.
The schematic layout which is shown in Figure 8.3 describes the stations, the work
process flow between stations which starts from Station 100 and ends with Station 320.
The mathematical modeled layout describes the work stations can be best summarized
in Table 8.1 and Figure 8.4. The door assembly process generally involves loading
process, welding, hemming and curing process before it is assembled onto the Body in
White (BIW). It is operated by a total of 4 operators located in the 3 loading and 1
unloading stations to load the sub-assemblies onto the fixtures at Station 100, 140, 200
and 320 of the production line. Total of 95 spot weld location are required per door.
The sequence of parts joint according to process and stations can be understood from
Figure 8.1. The longest process is the hemming process which is 129 seconds per unit
door. Table 8.1 illustrates the equipment, welds and cycle time of each station of the
door process.
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8.1. JLR DOOR MANUFACTURING SYSTEM DESCRIPTION
Figure 8.1: Current Assembly Sequence of Front door for model.
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8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
S1
3
5
9
9
4
S2
2
6
8
140
100110120
S3
160
220190
150
S4
1
300
210200
310
320
Usage/Product Component ID Component Name
1 1 PNL DR O/S R/LH (3 Dr )
1 2 CHAN FRT DR WDO GL R/LH (Common 3 Dr/5Dr )
1 3 PNL FRT DR I/S R/LH (3 Dr)
1 4 REINF DR I/S PNL OPNG R/LH (3 Dr )
1 5 REINF DR I/S PNL @ LAT R/LH (Common 3 Dr/5Dr )
1 6 REINF FRT DR O/S PNL @ BELR/LH (3 Dr )
1 7 PLT ASY DR HGE (COMMON 3 & 5 Dr)
1 8 STRN DR O/S PNL R/LH (3 Dr )
2 9 PLT ASY DR HGE (COMMON 3 & 5 Dr)
JLRZ18_3Dr_Model
Precedence Diagram
Figure 8.2: Precedence Diagram for the front door assembly line for the current config-
uration.
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NFigure 8.3: Schematic layout of current manufacturing system for assembly line of right and left front door (identical systems).
167
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
Figure 8.4: Current manufacturing system model of the door assembly system.
In this section we explain the synthetic description of operations in Front Door As-
sembly line in more details. The operations synthetic is summerized also in Figure
8.5.
Station 100. Operator 1 picks up the inner panel from the corresponding racks and
loads to geo welding. Then, Operator 1 pushes the start button that starts the clamp
and performs pin engagement. Operator 1 loads and clamps each of the other 5 parts
one at a time. When the loading of the 6 parts is finished, he pushes a start button to
close the shutter door and he moves to station 140. The start button causes the robot
100R1 to begin tack welding when tack welding finishes 100R2 unloads the assembly
from geo station and cones the latch plate.
Station 110. Robot 100R2 moves to station 110 from station 100 in order to load
the assembled panel the geo of Station 110 and after loading comes back to Station
100. Afterward, robot 110R1 starts tack welding the while turn table position the
part properly. After tack welding, clamps and pins are automatically retracted. 120R1
moves from next station (station120) to this station in order to unload the part to
station 120.
Station 120. 120R1 re-spot welds and moves the inner panel to station 140.
Station 140. While stations Stn110 and Stn120 was working on inner panel OP1
who previously worked in Station 100 left there, loads three more parts, Glass channel,
Waist rail and Intrusion beam. The roller shutter door closes after OP1 complete
loading and OP1 goes back to Station 100. Robot 140R1 unloads these three parts and
moves them to Station 150.
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8.1. JLR DOOR MANUFACTURING SYSTEM DESCRIPTION
Figure 8.5: Graphical operation synthetic description
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8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
Station 150. Two paths come to this station, the first from Station 140 (three
additional parts) and then Station 120 (Inner panel). 150R2 starts geo welding (17
spots) and 150R1 joins into the geo welding after the first 8 spots. 150R1 and 150R2
move to home position, and then 150R3 unloads inner sub assembly from Station 150
in order to load to Station 160 which is deposit. [In this stage inner panel is almost
complete and the only operation left in anti-flutter operation which will be performed
before the hemming process which joints inner panel and outer panel.]
Station 160. In each cycle time, each inner sub-assembly panel will be loaded to
deposit by 150R3 and spends around 23 Seconds there (17% of Cycle Time). Robot
140R1 unloads inner sub-assembly panel and moves to Station 190.
Station 190. This station includes ”PUT DOWN ” and ”Date Stamp”. First,
140R1 loads the PUT DOWN with the inner panel and then 190R1 unloads from PUT
DOWN (2 seconds after loading by 140R1). 190R1 applies Date Stamp and moves to
Station 220 which is the next station for inner panel before joining the outer panel.
Station 220. 190R1 applies the anti-flutter operations to three welding beads.
Station 200 (outer panel loading). Operator 2 loads the outer panel to the station
from the corresponding rack. He pushes the start button which closes the roller shutter
door. Then, OP2 goes to Station 320. Robot 200R1 unloads the part from Stn200 in
order to go to Station 210.
Station 210. Robot 200R1 applies hem sealer on two different position of the outer
panel and moves to Stn300.
Station 300. Inner sub-assembly panel comes to this station by means of 200R1
and outer panel by means of 190R1 from their respecting manufacturing flow. 300R1
performs hemming, which results in joining two panels and moves the unified part to
Station 310.
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8.1. JLR DOOR MANUFACTURING SYSTEM DESCRIPTION
Station 310. 300R1 loads the curing machine and goes back to its home position.
After the curing operation is done, 310R1 unloads the curing machine and loads the
exit conveyor.
Station 320. Operator 2 who walked to this station after loading the outer panel in
Station 200 performs sealer wiping and loads the final part to the completed part rack
and turns back to Station 200.
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Equipment Welds
Station Description Turntable/
Fixture
Handling/
Hemming
Robot
Weld
Robot
PED
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Tack
Weld
Spot
Weld
Cycle
Time
Operator
No.
100 Loading 1 1 1 10 121 1
110 RSW 1 1 13 12 128
120 RSW 1 1 30 95
140 Loading 1 2 44 1
150 RSW 1 2 19 11 118
160 Loading 1 38
190 Buffer 31
200 Loading 1 28
210 Adhesive 1 1 31
220 Anti-Flutter 1 1 21
300 Hemming 1 3 129
310 Curling 2 1 112
320 Unloading, QC 116 2
Total 9 10 4 3 42 53 4
Table 8.1: Current Manufacturing System Station Description.
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Table 8.2 represents the analyzed data from the company data base to extract the re-
quired parameters; p is the failure rate of the station, r is the repair rate of the station,
CT is the cycle time of the station, mu is the processing rate of the station, i.e. 1/CT ,
the iso-throughput is the isolated production rate of the station, i.e. the production
rate the station would have if it was completely isolated from the rest of the line, i.e.,
without considering the impact of the neighboring machines and buffers, and e is the
isolated technical efficiency of the station, i.e., the fraction of time the machine is op-
erational, again if not impeded by other machines in the system.
The current configuration of the mentioned system, only involving RSW technology
was modeled and evaluated with the analytical method, grounding on the reliability
data which is provided by the robots manufacturer while designing their plants. The
studied manufacturing system currently includes two identical systems, one dedicated
to the production of front left doors, and one dedicated to the production of front
right doors. The total throughput of the system under the current configuration is
0.4553 part/min, corresponding to a 27.318 job per hour [JPH]. This follows 27.318
front right door per hour and 27.318 front left door per hour. According to the quality
control sector of the company, all the assembled part are conforming. This means the
system yield is equal to 1. Therefore, the effective throughput of the system is equal
to the total throughput and its equal to 0.4553 for each side front door. This has to
be considered as the target throughput for the proposed configuration of this system,
since the current configuration is able to meet the requirements of the body production
line. The system bottleneck (station with the smallest isolated production rate) is the
hamming station (Station 300). Its isolated throughput (0.4631 parts/min) represents
the maximum possible achievable production rate in the system.
8.2 The New Configuration of Assembly System: Appli-
cation of Remote Laser Welding
The robot supplier of the JLR company proposed to apply the remote laser welding
technology for some of the important joints of the door during the assembly. In the
proposed configuration number of robots are reduced from 14 to 8 and the design of
sub-assemblies slightly changed. In fact, the resistant spot welding technology is not
173
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
Station ID p r CT mu iso mu e
1 ST 100 0,001313 0,2 1,26 0,7937 0,7885 0,9935
2 ST 110 0,00076 0,2 1,7 0,577 0,5748 0,9962
3 ST 120 0,000791 0,2 1,94 0,5155 0,5134 0,9961
4 ST 140 0,000553 0,2 0,6 1,7857 1,7808 0,9972
5 ST 150 0,001965 0,2 2,03 0,4926 0,4878 0,9903
6 ST 190+220 0,000553 0,2 0,85 1,1765 1,1732 0,9972
7 ST 200+210 0,000553 0,2 0,908 1,1013 1,0983 0,9972
8 ST 300 0,000872 0,2 2,15 0,4651 0,4631 0,9957
9 ST 310 0,000715 0,2 1,733 0,577 0,575 0,9964
10 ST 320 0,000207 0,2 1,556 0,6427 0,642 0,999
Table 8.2: Summary of parameters of the current manufacturing system, adopted for
analytical performance measurement method.
completely removed, but the new configuration proposes the hybrid system including
both resistant spot welding and the remote laser welding. The assembly sequence is
changed. The precedence diagram represented in Figure 8.6 shows the new assembly
sequence of sub-assemblies.
In the new proposal of the system, the Remote Laser Welding (RLW) station is shared
between the two part types, the left front door and the right front door. The RLW
robot is welding the right front door in each cycle time and then it turns to left front
door line, welding the left door. Due to the fast processing rate of the RLW robot,
before the next sub-assembly of the right side appears in the RLW station, the RLW
robot finishes the left door and returns to the right side again. In this thesis we focused
only on the production system of the right front door. The proposed layout is presented
in Figure 8.7. The new configuration is designed to be run by two operators, one ded-
icated to each part type (left and right front doors). The synthetic feature of the new
configuration is reported in Table 8.4. The proposed configuration saves 6 robots for
each of the symmetric line, which is 12 robots for the whole system. Therefore, the
resulting system saves 40% in terms of number of robots.
The parameters of the stations which characterizes the machines reliability data is pro-
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8.2. THE NEW CONFIGURATION OF ASSEMBLY SYSTEM:APPLICATION OF REMOTE LASER WELDING
Figure 8.6: Precedence Diagram for the front door assembly line for the new configuration.
175
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
vided in Table 8.3. The manufacturing model of the proposed hybrid configuration,
including the RSW and RLW, is represented in Figure 8.8. The considered system is
shown by the red squared line, which is the right front door assembly system. The
performance of the current system is evaluated by the analytical model based on de-
composition method which supports the performance evaluation of the assembly system
with continuous flow of material and continuous time. The obtained results are pro-
vided in Table 8.6. As it can be noticed, although the robots are reduced by 40% in
both lines, but as it can be noticed the effective throughput is lower than the target
effective throughput, which is 0.4553 [part/min]. Therefore, we have applied the selec-
tive assembly method for RLW assembly station to improve the effective throughput
of the proposed configuration.
176
8.2. THE NEW CONFIGURATION OF ASSEMBLY SYSTEM:APPLICATION OF REMOTE LASER WELDING
Station ID
Fail-
ure
Modes
p r CT [min] mu e iso e
ST 1 1 0,00022 0,25575 2,08333 0,48000 0,99898 0,47951
2 0,00002 0,25083
3 0,00005 0,46371
4 0,00172 1,00000
ST 2 1 0,00014 0,27822 2,03333 0,49180 0,99949 0,49155
ST 3 1 0,00048 0,25575 1,46667 0,68182 0,99951 0,68148
2 0,00004 0,37097
3 0,00028 1,00000
RLW 1 0,00155 0,28536 1,85000 0,54054 0,99814 0,53954
2 0,00002 0,25083
3 0,00006 0,33387
4 0,00007 0,45240
5 0,00007 0,25575
6 0,00153 0,20000
ST 5 1 0,00050 0,27822 1,93333 0,51724 0,99937 0,51692
2 0,00030 0,25575
3 0,00010 0,19787
4 0,00003 0,37097
5 0,00001 0,30242
6 0,00008 0,21078
ST 200+210 1 0,00055 0,20000 0,90800 1,10132 0,99724 1,09828
ST 300 1 0,00087 0,20000 2,15000 0,46512 0,99566 0,46310
ST 310 1 0,00072 0,20000 1,73300 0,57703 0,99644 0,57498
ST 320 1 0,00021 0,20000 1,55600 0,64267 0,99897 0,64201
Table 8.3: Summary of parameters of the proposed manufacturing system, adopted for
analytical performance measurement method
177
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Figure 8.7: The layout representing the new hybrid configuration.
178
8.2
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Activity Cycle Description Begin Duration [sec.] End
Station 100
Smart Laser Laser Welding RH door (56 stitches) 0,0 37,0 37,0
Smart Laser Laser Dimpling RH door (168 dimples) 37,0 27,0 64,0
Smart Laser Laser Welding LH door(56 stitches) 64,0 37,0 101,0
Smart Laser Laser Dimpling LH door (168 dimples) 101,0 27,0 128,0
Table Turn 180 0,0 5,0 5,0
Dimple fixture Open 5,0 4,0 9,0
120 R1 Unload parts from St 140 welding fixture 9,0 8,0 17,0
120 R1 Load parts on st 140 welding fixture 17,0 10,0 27,0
120 R1 Load parts to St 150 27,0 10,0 37,0
100 R1 Unload inner panel dimpled from st 140 dimple fixture 9,0 8,0 17,0
100 R1 Load inner panel on st 140 dimple fixture 17,0 10,0 27,0
100 R1 Load inner panel dimpled on st 140 welding fixture 27,0 8,0 35,0
Dimple fixture Close 35,0 4,0 39,0
Table Turn 180 39,0 17,0 56,0
100 R1 Change tool 35,0 19,0 54,0
100 R1 Welding respot (5 WS) OP130 54,0 15,0 69,0
100 R1 Move to st 110 69,0 2,0 71,0
100 R1 Welding geo spot (9 WS) 71,0 27,0 98,0
100 R1 Change tool 98,0 19,0 117,0
100 R1 Move to st 100 117,0 2,0 119,0
100 R1 Unload parts from loads St 100 119,0 8,0 127,0
100 R1 Move to st 140 127,0 2,0 129,0
120 R1 Move to st 120 37,0 2,0 39,0
120 R1 Unload parts from St 120 39,0 10,0 49,0
120 R1 Move to st 150 49,0 2,0 51,0
120 R1 Unload parts from St 150 69,0 8,0 77,0
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120 R1 Move to St 160 & Coning 77,0 16,0 93,0
120 R1 Move to St 170 Untiflutter (1020mm) 93,0 21,0 114,0
120 R1 Move and load on st 180 114,0 11,0 125,0
120 R1 Move to st 140 125,0 3,0 128,0
Station 120
OP1 Load 4 parts 0,0 32,0 32,0
OP1 Push button 32,0 2,0 34,0
OP1 Walk to st 110 34,0 4,0 38,0
Station 110
OP1 Load 3 parts 38,0 24,0 62,0
OP1 Push button 62,0 2,0 64,0
OP1 Walk to st 100 64,0 4,0 68,0
Table Turn 180 64,0 5,0 69,0
Table Turn 180 98,0 5,0 103,0
OP1 Unload part 103,0 8,0 111,0
OP1 Push button 111,0 0,0 111,0
OP1 Walk to st 120 111,0 4,0 115,0
Station 100
OP1 Load 1 parts 68,0 8,0 76,0
OP1 Push button 76,0 2,0 78,0
OP1 Walk to st 110 78,0 4,0 82,0
Table 8.4: Operation Synthetic of the new hybrid proposal including both RLW and RSW
180
8.3. THE NEW CONFIGURATION OF HYBRID SYSTEMINCLUDING SELECTIVE ASSEMBLY SYSTEM
Performance Measure Mean
TH Total 0,46235
TH Effective 0,35225
System Yield 0,76188
WIP 7,43
Table 8.5: Performance measures of the proposed manufacturing system with no-selective
assembly system.
8.3 The New Configuration of Hybrid System including
Selective Assembly System
Although the total throughput of the proposed hybrid configuration is higher than the
target throughput, but the system yield of the proposed system is not sufficient to
generate the effective throughput as much as required by the company. Therefore we
proposed to apply the selective assembly system to improve the ratio of the conform-
ing parts, resulting in higher effective throughput. The new configuration proposes to
classify the inner panel and the halo sub-assembly (which is processed through spot
welding in station 1) according to their key quality characteristics by means of the new
measurement device. The inner panel and the halo sub-assembly will be welded by
RLW smart laser in the assembly station, which is represented in Figure 8.9.
In order to classify the sub-assemblies we need to analyze the key characteristics of
the sub-assemblies that influence the laser welded stitches quality. Within the RLW
process the main source of error have been identified which is the part induced errors
due to the fact that the sheet-metal parts (both sub-assemblies) are manufactured by
stamping/forming processes. Manufacturers using traditional process control charts
to monitor their sheet metal stamping processes often encounter out-of-control signals
indicating that the process mean has changed. Unfortunately, a sheet metal stamping
process does not have the necessary adjustability in its process variable input settings
to allow adjusting the mean response in an out-of-control condition. Indeed, stamping
dies and presses have several input variables, such as tonnage, shut height, press par-
allelism, counterbalance pressure, nitrogen pressure in dies, press speed. Variation of
those parameters, combined together, might affect the final quality of the stamped part.
181
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
Figure 8.8: Proposed configuration for left front and right front door including RLW
station with normal assembly system, focusing on the right front door.
Unfortunately, stamping processes have no simple adjustment mechanisms to change
feature dimensions. Moreover, most stamping processes run out of statistical control.
Thus, manufacturers have difficulty determining the true long run process variation
and the inherent variability in die setup operations for a batch of parts. Majeske and
Hammett [2003] suggested decomposing stamping variation into three components: (I)
part-to-part, (II) batch-to-batch, and (III) within batch variation. The part-to-part
variation represents the short run variability about a given stable or trending batch
mean. The batch-to-batch variation represents the variability of the individual batch
mean between die setups. The within batch variation represents any movement of the
process mean during a given batch run.
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8.3. THE NEW CONFIGURATION OF HYBRID SYSTEMINCLUDING SELECTIVE ASSEMBLY SYSTEM
Figure 8.9: Proposed configuration including the selective assembly system of two classes
for right side front door.
In industrial SPC applications, the quality of manufactured products is evaluated by
Key Quality Characteristics identified by manufacturing engineers. Traditionally, these
characteristics have been physical measures, such as dimensions or part feature loca-
tions. These dimensional quality characteristics are of fundamental importance in as-
sembly, since variation in parts may lead to significant problems during the assembly
process, resulting in poor performance of the final product. Therefore, it is vital that
each part is within the specification limits for ease of assembly; ideally, the products
quality characteristics should be as close as possible to their corresponding target val-
ues. Traditionally, the choice of the Key Quality Characteristics was restricted by the
capabilities of the available measurement technologies. For example, consider the as-
sembly of car doors, where an inadequate door fit leads to a loss of quality, possibly
characterized by excessive door closing effort, increased wind noise, and/or decreased
aesthetics. Wells et al. [2012] noted that the quality of a doors fit is a function of
dimensional variations in the doors, body openings, and fitting and hanging processes.
To assess the fitting quality, engineers must decide on what to measure on the assem-
bly and how to interpret the data. Typically, quality inspection practitioners select
between 50 and 100 sampling points per door, track these points using Coordinate
Measuring Machines (CMMs), and then apply SPC methods to assess if the observed
vehicle-to-vehicle variation is significant Wells et al. [2011]. However, these sampling
points may not capture all possible variation sources since only some gaps between the
183
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
door and the body are measured.
Therefore, it is important to develop SPC methods that can better monitor the qual-
ity of such complex products, especially since increased variation in product quality is
often an indication of process deterioration. For example, in RLW applications it is
crucial to determine the variation of functional features (i.e., part-to-part gap at flange
areas) in order to assess the quality of the laser welded joints.
Advanced measurement technologies provide the opportunity to collect millions of data
points, allowing for a products entire surface geometry to be represented. With this
type of data, fault detection is no longer limited by traditional measurement system
capabilities. By monitoring the entire surface geometry one can detect the occurrence
of unexpected fault patterns, i.e. faults that would not normally impact pre-set CMM
measurement points Wells et al. [2012].
Three-dimensional surface-based scanners have recently emerged as a measuring tech-
nology that can rapidly provide such information. Son et al. [2002] showed that the
current focus for 3D scanners resides in reverse engineering applications and provid-
ing one-to-one comparisons between manufactured parts and their corresponding CAD
representations. Despite the importance of such comparisons, they only provide infor-
mation for a single scanned product, rather than capturing the part-to-part or batch-
to-batch variation, which is necessary for an accurate depiction of the state of the
manufacturing process. Therefore, surface-based scanner is a promising technology to
monitor the entire surface geometry and to detect the occurrence of unexpected fault
patterns.
Due to the fact that the data regarding the sub-assemblies measurement is confidential
for the company, in this thesis we have considered the limited data for analyzing the
effect of selective assembly system without lose of generality. According to the ana-
lyzed data regarding the stitches, we found out that there is a critical stitch which is
considered as the key quality characteristic of the final assembly. In order to meet the
required tolerance on this stitch, there is a single point on each sub-assembly that is
pointed as the key characteristics of each sub-assembly. The provided measurement
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8.3. THE NEW CONFIGURATION OF HYBRID SYSTEMINCLUDING SELECTIVE ASSEMBLY SYSTEM
Figure 8.10: Proposed configuration including the selective assembly system of three
classes for right side front door.
data form sampling of each sub-assemblies depicts the Gaussian distribution for the
variation regarding the nominal value. Therefore, for the process variation of each
sub-assembly we considered the Gaussian distribution based on the sampling data. For
halo sub-assembly the critical point geometry is distributed as N(0.4474, 0.0442) and
for the inner panel sub-assembly is distributed as N(0.24, 0.052). We have modeled in
simulation the proposed configuration for selective assembly of 2 classes and 3 classes.
Figure 8.10 represents the hybrid system model with selective assembly station of 3
quality classes for remote laser welding station. It must be noticed that, the total
buffer space for selective assembly of 2 classes and 3 classes is equal to that of baseline
configuration. Classification for selective assembly of 3 quality classes is based on the
equal probability approach for both sub-assemblies. Table 8.6 shows the results of the
proposed system for selective assembly of 2 classes and 3 classes. As it can be noticed
the effective throughput obtained by the proposed selective assembly with 2 quality
classes is smaller than 0.4553 [part/min], therefore we analyzed the selective assembly
system with 3 quality classes. As it can be expected, the total throughput of the system
is reduced due to the logistic complexity while the system yield is increased. As the
effect of this competing effect, the effective throughput of the proposed system with 3
quality classes is 0.4565, which is slightly higher than the target effective throughput.
185
8. SELECTIVE ASSEMBLY APPLICATION IN AUTOMOTIVEINDUSTRY: DOOR ASSEMBLY IN JAGUAR AND LAND ROVERCOMPANY
TH Tot. CI TH Eff CI Yield CI WIP CI
2
Classes0,46219 0,0005 0,41585 0.0008 0,89975 0,00106 21,6 2,858
3
Classes0,46069 0.0009 0,4565 0,00107 0,9909 0,00128 18 4,919
Table 8.6: Performance measures of the proposed manufacturing system for selective
assembly system of 2 and 3 quality classes.
186
9
Conclusion
In this thesis we have explored and analyzed the behavior of the selective and adaptive
assembly systems in an integrated framework of quality and system logistic performance
for the first time. The system level analysis of selective assembly system is performed
through a new analytical method in addition to the developed simulation model of
the selective assembly systems. The provided results of the analytical model show the
good accuracy of the method and the modeled system comparing to the simulation re-
sults. Beside, in this thesis we proposed to apply the production adaptability strategy
to improve the system performance of selective and adaptive assembly system. The
optimal process adaptability method is provided and the system effect of such a design
has been analyzed through the simulation model. Moreover, important insights have
been derived by the application of the selective assembly system in a real case which
open new way of designing the assembly system, jointly considering the quality and the
system logistic aspects.
The main achievements and results of this thesis can be summarized in the following
key considerations:
• An innovative modeling framework for selective assembly systems that integrates
quality and production logistics features is developed. A new approximate ana-
lytical method is developed for the performance evaluation of this systems. The
provided results show that the developed method is accurate while estimating
187
9. CONCLUSION
the main system performance measures and can be used to support the design of
these complex systems in real manufacturing settings.
• The developed analytical method is applied to observe the system behavior of
the selective assembly systems when the total buffer space is increased. The
results show that although the selective assembly system provides a higher system
yield with respect to the non-selective assembly system, but it affects negatively
the total throughput of the system. It is shown that the total throughput of
the system increased as the total buffer space increases, but due to the logistic
complexity of the selective assembly system the total throughput of this system is
reduced compared to the non-selective assembly system. It is important to notice
that the negative effect of selective assembly system on the total throughput
become less evident as the total buffer space increases. The combined result
of increased yield and decreased total throughput is the remarkable increase of
the effective throughput with respect to the traditional, non-selective, assembly
system. In addition, the positive effect of the selective assembly system on the
effective throughput of the system is even more visible as the total buffer size
increases.
• In order to explore the behavior of the selective assembly system under more
quality classes, we have developed a simulation model. The results of the simula-
tion show that although the total throughput is reduced as the number of quality
classes increases, the system yield is increased, as the number of quality classes
increases. As a result of this competing effect, the effective throughput curve is
concave, it is increasing until a certain point and then it starts decreasing. Thus,
being concerned with the concave behavior of the effective throughput curve, it il-
lustrates that there is an optimal point to select for the number of quality classes.
Therefore, in order to make a proper decision for design of selective assembly
systems in terms of number of quality classes, there is an absolute need to ob-
serve the trad-off between the total throughput and the system yield through the
resulting effective throughput.
• we have analyzed and explored the behavior of the selective and adaptive assembly
systems. In particular, we have applied the process adaptation in the manufac-
turing process in order to reduce the discard rate of sub-assemblies. The proposed
188
method is modeled within the analytical performance measurement framework of
the selective assembly systems which is addressed in previous chapters. More-
over, the proposed optimal process adaptation design is addressed. Finally, we
illustrate the effect of process adaptation in system level performance of selective
and adaptive assembly systems. We have shown that the optimal process adap-
tation design can considerably reduce the WIP while increase the throughput of
the system.
• Although the process adaptations are significantly beneficial to increase the effi-
ciency of the selective assembly systems, but not all the manufacturing processes
are able to produce with several mean target values. Therefore, we proposed new
intelligent flow control policies, based on the observable system states, to handle
better the logistic complexity of the selective assembly systems in deadlock states.
The key goal of these policies is to reduce the discard rate, thus we concluded that
the proposed policies are out-performing the Discard Policy which is proposed in
the literature, considering the discard rate of sub-assemblies.
• The application and benefits of implementing selective assembly systems in pro-
duction of the electrical engines in Bosch company is shown in the chapter 7.
The results of the proposed approaches are published as deliverable of EU funded
project (MuProD [2013d]), MuProD “Innovative proactive Quality control sys-
tem for in-process multi-stage defect reduction”. We have shown that there ex-
ist an optimal number of quality classes that maximizes the throughput of the
conforming assemblies. This suggests that, according to the number of quality
classes of selective assembly and the resulting quality and productivity parame-
ters, the system designer should configure the selective assembly system to reach
the maximum of effective throughput curve, without considering the system yield
and total throughput behavior separately. In addition, we showed that the vari-
ance of the generated magnetic flux intensity decreases as the number of quality
classes increase, but by observing the effective throughput we realized that the
optimal configuration is the selective assembly system with two quality classes
and considering only the reduced variance of the final assembly key characteristic
obtains the configuration that sub-perform the optimal configuration. It is also
shown that as the tolerances on the key characteristic of final assembly becomes
189
9. CONCLUSION
tighter, selective assembly system with more quality classes are out-performing
more effectively.
• The final chapter is associated with the formalization, modeling, and application
of selective assembly system in the current body-in-white manufacturing system
of Jaguar and Land Rover company corresponding to door production. The new
technology regarding to the welding, remote laser welding, is proposed for the
door production manufacturing system. We showed that the proposed manufac-
turing system cannot provide the effective throughput as required by the company
when selective assembly system is not applied. Therefore, the application of the
selective assembly system to control part-to-part gap is shown and the benefits
of this system is provided.
Future research will be focused on the extending of the proposed analytical method for
the selective assembly systems with more quality classes. The methodological frame-
work is the same as the method applied for the two classes selective assembly system.
The attention will be focused on the integration of the proposed method into the long
transfer lines. Moreover, the analytical method could be extended to evaluate the se-
lective assembly system performance for assemblies with more than two sub-assemblies.
The proposed intelligent flow control policies to manage better the deadlock states will
be integrated into the analytical model. Finally, the method can be applied to other
manufacturing context such as battery production.
190
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