Upload
christopher-salazar
View
220
Download
0
Tags:
Embed Size (px)
Citation preview
Impact of Statistical Process Impact of Statistical Process Control (SPC) on the Control (SPC) on the
Performance of Production Performance of Production SystemsSystems
M. Colledani, T. TolioM. Colledani, T. Tolio
Dipartimento di MeccanicaSezione Tecnologie Meccaniche e Produzione
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
Outline of the presentationOutline of the presentation
1- Literature review2- Problem definition
3- Isolated machine with local monitoring4- Two machines one buffer with local monitoring5- Two machines one buffer with remote monitoring 6- Long lines with local monitoring
7- Numerical results8- Conclusion and future research
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
1- Literature Review1- Literature Review- Montgomery,D.C, Introduction to Statistical Process Control, John Wiley and Sons, Inc, 1991. - Ho C., Case K., Economic Design of Control Charts: A Literature Review for 1981-1991, Journal of Quality Technology, 26,: 39-53,1994.- Raz T.,” A Survey of Models for Allocating Inspection Effort in Multistage Production Systems”, Journal of Quality Technology, 18-239-246, 1986. - Dallery, Y.,Gershwin, S.B., “Manufacturing Flow Line Systems: A Review of Models an Analytical Results, Queueing Systems Theory and Applications, Special Issue on Queueing Models of Manufacturing Systems, 12(1-2). 1992. - Gershwin S.B., Matta A. and Tolio T., Analisys of Two Machine Lines with Multiple Failure Modes, IIE Transaction, 34(1) : 51 - 62, 2002.
- Gershwin S.B., Kim J.,Integrated Quality and Quantity Modeling of a Production Line”, OR Spectrum, 2005. - Colosimo B.M., Semeraro Q. and Tolio T. “Designing X bar Control Charts in Multistage Serial Manufacturing System, CIRP Journal of Manufacturing Systems, 31-6, 2002 - Tempelmeier H., Burger M, Performance Evaluation of Unbalanced Flow Lines with General Distributed Processing Times, Failures and Imperfect Production, IIE Transactions,33,293-302, 2000.- Helber S. Performance Anaiysis of Flow Lines with Non-Linear Flow of Material, Springer, 1999.
- Inman R., Blumenfeld D., Huang N. and Li J..,” Designing Productivity Systems for Quality: research opportunities from an automotive industry perspective “, IJPR, 41(9), 2003.
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
t )IID(0,~ 2
tY
Example
2- Process in Statistical control
PROCESS IN CONTROLPROCESS IN CONTROL each quality measure is in a statistical control state.
STATISTICAL CONTROL STATESTATISTICAL CONTROL STATE is a state where all the variations within the observed data can be related to a set of causes not identifiable which do not change over time (i.e. the distribution is stable)
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
2- Specifications and bad parts
t
Lower Specification Limit - LSL
Upper Specification Limit - USL
Even if the process is in control it can produce bad parts.
However, if the process goes out of control the number of bad parts produced changes (in general, infinite out of control modes are possible).
LSL
USL
t
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
2- Detecting out of control states
In order to understand if the process is in control or out of control, we can sample the produced parts (in the extreme case we can have 100% inspection). Then we measure the parts in the sample and we perform a statistical test with the following hypotheses.H0: the process is in control
H1: the process is out control
The outcome of the test is subject to two types of errors:
error: the process is in control but the test detects an out of control (false alarm)
error: the process is out control but the test does not detect it (out of control not detected)
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
If the process is out of control
2- Detecting out of control states
1
ARL0 1
1ARL1
If we repeat the test many times and each test has the same and errors than we can evaluate the average number of samples we have to take in order to have an alarm (ARL = Average Run Length).
t t
If the process is in control
4.370ARL0.0027 0 For example:
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
2- Detecting out of control statesIf we consider a single machine in isolation and a control chart attached to it then how many parts does the machine produce before getting an alarm?
Let us define:m the sample size.h the number of parts produced between two samples.
)(1
mh
1
1m) (h
β
If the process is out of controlIf the process is in control
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
2- Inspection stationsTesting allows to draw information on the process but also on the inspected parts.
•Inspected parts which are within the specification limits may proceed downstream (if testing does not destroy the parts).•Inspected parts which are outside the specification limits may be either scrapped or reworked
Therefore the logic at an inspection station decides two things:
•control charts which send the alarms related to the out of control conditions•scrap/rework policies which decide the final destination of the inspected parts
qMqiC ,
scrap
rework
good(If m=1 and h=0 than 100% inspection is performed). qi
Out of control
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
2- Some Assumptions of the Model2- Some Assumptions of the Model-The flow of material in the system is considered as discrete.-Each machine is characterized by the same processing time, scaled to time unit.-Buffers have finite capacity.-Machines can be of three types: manufacturing machines, inspection machines or integrated machines.-Inspection machines are perfectly accurate.-Failures and shifts to out of control are Operation Dependent. -Once an out of control has been detected, the time to repair it is geometrically distributed.-Machines can fail in different modes. We identify two classes of failures:
-f type local failures: are those for which the repairing intervention also set the machine to the in control state; type local failures: are those for which the repairing intervention reset the machine to conditions it had before the failure occurred.
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
3- Modelling a single machine in isolation Wi: operative in control
Di,fi: f type local down stateDi,i: type local down stateAi
1: out of control detected but not realAi
2: out of control detected and real Oi: out of control non
detected
1iA)( ,qi
falsei Cp
ifiD , iO
2iA
)( ,qii Cp
qualityip
falseir
qualityirifip .
fiir .
iW
i
i
WiD ,
fiip .
iir .
iip .
iir .
iip .
i
i
OiD ,
)]()()[(
1
)(
1)(
,,,0,,
qiqiqiqiiqi
false
CmChCARLCMTTFACp
i
Quality link equations:
)]()()[(
1
)(
1)(
,,,1,,
qiqiqiqiiqii CmChCARLCMTTD
Cp
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
3- The Isolated Machine Case3- The Isolated Machine CaseOnce the Markov chain has been solved and all the state probabilities have been calculated, the performance measures for the single machine case can be derive as follows:Total average production rate: )()( ii
TOT
i OWE
Effective average production rate: )1)(()1)(( ii Oii
Wii
EFF
i OWE
System yield (fraction of conforming parts produced):
)()(
)1)(()1)((
ii
Oii
Wii
TOT
i
EFF
ii OW
OW
E
EY
ii
Average production rate of parts to be scrapped:
Average production rate of parts to be reworked:
SOsii
SWii
S ii OWE ,,
, )()(
RWOii
RWWii
RW ii OWE ,, )()(
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
qM jMiB KMqiC , jjC ,
iM qBjB
RWjjB ,
RWqiB ,
scrap
rework
rework
scrap
4- The General Case4- The General Case
Quality has an impact on production system performance:
- Control charts allow to identify out of control states. The search for a cause for the out of control reduces the up time of the machine.- Scrap/rework policies allow to identify defective parts and to decide whether to scrap or to rework them.
The system architecture impacts on the quality system performance:- The presence of buffers causes a delay in the transmission
of the quality signal.
Total throughput Yield
Total throughput
Yield
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
CONVERGENCE
4- Two machine one buffer with local 4- Two machine one buffer with local monitoringmonitoring
C2,2
M2 B
1,1p 1,1r2,1p
2,1r
1,1 Fp1,1 Fr
1,2p 1,2r2,2p
2,2r
2,2 Fp2,2 Fr
M1
C1,1
This system is formed by two machines M1 and M2 locally controlled by C1,1 and C2,2.
MU(1) MD(1)
)1(1,1
Up )1(1,1
Ur
)( 1,1)1( CpU
false )( 1,1)1( CrU
false
)( 1,1)1( CpU )( 1,1
)1( CrU
)1(,1 1
UFp )1(
,1 1
UFr
)1(1,2
Dp )1(1,2
Dr
)( 2,2)1( Cp D
false )( 2,2)1( Cr D
false
)( 2,2)1( Cr D)( 2,2
)1( Cp D
)1(,2 2
DFp )1(
,2 2
DFr
B
Bfr2,2
)( 1,11 Cp
Bfr2,2qualityp1
falser1
qualityr11.1 fp
1.1 fr
)( 1,11 Cp false 11A
Bfp2,2 2
1A
1,1 fD 1O
1W
1
2,2W
fB
Bfp2,21.1 fp
1
2,2O
fB
)( 1,1)1( CpU
falseBfr2,2
1.1 fp
1.1 fr
)1(,1 UA
)1(,2 UA
)1(UW
)1(2,2
UfB
)1(1,1
UfD
)( 1,1)1( CpU
)( 1,1)1( CrU
false
)( 1,1)1( CrU
Bfp2,2
Markov chain solution
Stationary state
probability distribution
New failure probabilities calculation
Upstream pseudo-machine MU(1)
Building Block evaluation“Gershwin, Matta, Tolio 2002”
New blocking and
starvation probabilitiesUpstream machine
M1
Downstream machine M2
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
)1()()()()()1( 221121 EOWOWEEE TOTTOTTOT
Total average throughput:
System yield: TOTEYYY 21)1(
Average buffer level: )1(nn
Bfr2,2
)( 1,11 Cp
Bfr2,2qualityp1
falser1
qualityr11.1 fp
1.1 fr
)( 1,11 Cp false 11A
Bfp2,2 2
1A
1,1 fD 1O
1W
1
2,2W
fB
Bfp2,21.1 fp
1
2,2O
fB)1(
,...,1 ))1((
))1((
,,2
,2
,
,2
2
22
Dfj
Bf
djB
f
fjBf
j
j
rr
FfrE
Bp
Blocking (starvation) probabilities
equations
Monitored
machine model
)( 1,1)1( CpU
falseBfr2,2
1.1 fp
1.1 fr
)1(,1 UA
)1(,2 UA
)1(UW
)1(2,2
UfB
)1(1,1
UfD
)( 1,1)1( CpU
)( 1,1)1( CrU
false
)( 1,1)1( CrU
Bfp2,2
)()())1(( 11 OWW U
)())1(( 11
,1 AA U
)())1(( 21
,2 AA U
)()())1((
)())1((
1
2
1
22,2
11,1
,2,2
,1
Of
Wf
U
fU
BBB
DD
f
f
Stationary state probability distribution
)()()(
)()(
))1((
))1(()( 1,1
)1(
11
11
1,1)1(
,1
1,1)1( Cr
OW
ACr
W
ACp UU
U
U
Ufalsefalsefalse
)()()(
)()(
))1((
))1(()( 1,1
)1(
11
21
1,1)1(
,2
1,1)1( Cr
OW
ACr
W
ACp UU
U
U
U
falseU rCr false 11,1)1( )(
Transition probabilitiesFalse alarm state:
qualityU rCr 11,1)1( )(
Detected out of control state:
Pseudo-machine model
4- Two machine one buffer with local 4- Two machine one buffer with local monitoringmonitoring
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
C 1,2
M 2
B
1,1p
1,1r
2,1p
2,1r
1,1 Fp
1,1 Fr
1,2p
1,2r
2,2p
2,2r
2,2 Fp
2,2 Fr
M 1
Monitored machine MiControl chart Ci,q (i<q)
p1,2delay represents the delay of the quality information due to the
presence of the finite capacity buffer B. It can be calculated by using the following equation:
1E
ndelay En
E
delaypdelay
12,1
5- Two machine one buffer with remote 5- Two machine one buffer with remote monitoringmonitoring
A12: out of control correctly
detected by the control chart (i<q)
O11: out of control, not
detected stateO2
1: out of control, detected if the machine was locally monitored (i=q)
Additional states:
The approach remains the same as in the previous case, only the Markov chain is more complicated:
Bfr2,2
)( 1,11 CpB
fr2,2
qualityp1
falser1
qualityr11.1 fp
1.1 fr
)( 1,11 Cp false 11A
Bfp2,2 2
1A
1,1 fD 11O
1W
1
2,2W
fB
Bfp2,2
1.1 fp 11
2,2O
fB
21
2,2O
fB
21O
Bfp2,2
Bfr2,22,1
delayp
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
6- Long lines with local monitoring – 6- Long lines with local monitoring – the approachthe approach KKC ,1,1 iiCiiC ,2,2C1,1C
1iM1B 2B iB 1iBiM KM1M 2M
By solving the two locally monitored machines systems with the presented method and by using decomposition equations the
performance of the original line can be estimated.
As for the two locally monitored machines system, the approach follows a two level decomposition, since alternately the Markov chain representing each machine (machine level) and each building block (buffer level) are studied .
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
)1(DM)1(UM )1(B )2(B )2(DM)2(UM
)1(1,1
Up )1(1,1
Ur)1(
,1 1
UFp )1(
,1 1
UFr
)( 1,1)1( CpU
false)( 1,1
)1( CrUfalse
)( 1,1)1( CpU )( 1,1
)1( CrU
)( 2,2)1( CpU
false
)( 2,2)1( CpU
)1(1,3
Dp )1(1,3
Dr)1(
,3 3
DFp )1(
,3 3
UFr
)( 3,3)1( Cp D
false)( 3,3
)1( Cr Dfalse
)( 3,3)1( Cp D )( 3,3
)1( Cr D
)1(1,2
Dp )1(1,2
Dr)1(
,2 2
DFp )1(
,2 2
DFr
)( 2,2)1( Cp D
false)( 2,2
)1( Cr Dfalse
)( 2,2)1( Cp D )( 2,2
)1( Cr D
)1(1,3
Dp )1(1,3
Dr)1(
,3 3
DFp )1(
,3 3
DFr
)1(2,3 3
DFp
)1(2,3 3
DFr
)1(1,2
Up )1(1,2
Ur)1(
,2 2
UFp )1(
,2 2
UFr
)( 2,2)1( CrU
false
)( 2,2)1( CrU
)1(1,1
Up )1(1,1
Ur)1(
,1 1
UFp )1(
,1 1
UFr
)1(2,1 1
UFp
)1(2,1 1
UFr
Local failure probabilities: are simply equal to those of the correspondent machine in the original line.
Quality linked failure probabilities: can be evaluated by using quality link equations provided.Remote failure probabilities: can be evaluated by using the following decomposition equations. They acts exactly in the same way as type local failure modes for the pseudo-machines.
jj fjU
fj rir ,, )( 2,...,1,1,...,1 )()1(
)1()(
,
,
,
jj
UfjUfj Ffijir
iE
iPsip
jfj
j
j
jj fjD
fj rir ,, )( 2,...,1;,...1 )()1(
)1()(
,
,,
Kk
DfkDfk FfKikir
iE
iPbip
kfk
k
k
Upstream pseudo-machinesDownstream pseudo-machines
6- Long lines with local monitoring - 6- Long lines with local monitoring - failuresfailures
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
KKC ,1,1 iiCiiC ,2,2C1,1C
1iM1B 2B iB 1iBiM KM1M 2M
An iterative algorithm, inspired to the DDX, has been used to efficiently solve the decomposition equations. It behaves as follows, after the initialization phase:
- Visiting all the upstream pseudo-machines for i=2,..,K-1
- Unknown failures probabilities are calculated by using decomposition equations;- The performance of the building block l(i) are evaluated by using the two level approach used for the two monitored machines system;- The same steps are performed visiting all the downstream pseudo-
machines for i=K-2,..,1At the convergence, the system yield can be evaluated as:
)1(...)2()1( KYYYYsystem )()()( iYiYiY DU
K
ik
kD
i
j
jU YiYYiY
11
)( )(
totsystemsystem
eff EYE
The total and the effective average production rates:
)1(...)2()1( KEEEE totsystem
6- Long lines with local monitoring – 6- Long lines with local monitoring – the algorithmthe algorithm
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
7- Numerical Results – two locally monitored 7- Numerical Results – two locally monitored machinesmachinesMore than one hundred test cases with random parameters have been carried out and compared with simulation. Some of those cases randomly selected are reported:
CASE 1 2 3 4 5 6 7 8 9 10
CT 1.6780 0.955 2.4 2.4138 1.9848 5.1083 1.9835 3.023 18.429 1.4289
SIM 1.6648 0.939 2.386 2.399 1.9847 5.0487 1.9844 0.034 18.632 1.4244
n (1
)
e % 0.3295 0.199 0.343 0.35 0.0023 0.4969 0.0232 0.1813 0.9195 0.03
CT 0.6562 0.1532 0.3557 0.3563 0.4067 0.4301 0.4316 0.113 0.2804 0.5368
SIM 0.6575 0.1527 0.3559 0.3567 0.4088 0.4314 0.4434 0.114 0.2809 0.537
E_e
ff
e % 0.1864 0.336 0.049 0.134 0.5158 0.3047 0.649 0.8546 0.152 0.0275
CT 0.9115 0.2211 0.3755 0.3772 0.4259 0.6070 0.4612 0.4333 0.5735 0.5567
SIM 0.9132 0.2205 0.3753 0.3777 0.4280 0.6087 0.4642 0.4367 0.5743 0.5569 E
_tot
e % 0.1904 0.287 0.047 0.139 0.5057 0.2687 0.6618 0.7868 0.1372 0.0287
CT 0.7199 0.693 0.9472 0.9444 0.9550 0.7085 0.9359 0.261 0.489 0.9642
SIM 0.7199 0.6927 0.9473 0.9444 0.9551 0.7087 0.9358 0.2611 0.4891 0.9642
Yie
ld
e % 0.0038 0.048 0.0014 0.005 0.0100 0.0361 0.011 0.0689 0.0163 0.0005
System Yield Total E Effective E Buffer level Average 0.05 0.432 0.516 0.388
<1% 98 97 95 98 <2% 100 100 100 100
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
7- Numerical Results – one remotely 7- Numerical Results – one remotely monitored machine monitored machine
CASE 1 2 3 4 5 6 7 8
CT 6.5074 2.1908 2.2900 8.0193 1.2400 2.4120 2.2066 1.3486
SIM 6.5550 2.1900 2.2679 7.8694 1.2362 2.4526 2.2119 1.3583
n (1
) e % 0.3968 0.0205 0.5525 1.2493 0.0549 0.4058 0.1317 0.1210
CT 0.3384 0.9019 0.8995 0.9018 0.6497 0.4209 0.5395 0.2955
SIM 0.3344 0.9017 0.9008 0.9046 0.6421 0.4171 0.5386 0.2950
E_e
ff
e % 1.2171 0.0210 0.1444 0.3098 1.1703 0.9278 0.1622 0.1932
CT 0.6059 0.9124 0.9139 0.9236 0.6734 0.6225 0.5725 0.3311
SIM 0.6060 0.9121 0.9137 0.9235 0.6635 0.6260 0.5735 0.3299 E
_tot
e % 0.0191 0.0406 0.0216 0.0165 1.4851 0.5612 0.1701 0.3509
CT 0.5585 0.9884 0.9842 0.9763 0.9647 0.6762 0.9423 0.8927
SIM 0.5517 0.9886 0.9858 0.9795 0.9677 0.6662 0.9391 0.8941
Yie
ld
e % 1.2347 0.0203 0.1659 0.3264 0.3101 1.4974 0.3327 0.1565
System Yield Total E Effective E Buffer level Average 0.62 0.711 0.789 0.52
<1% 90 88 85 92 <2% 100 100 100 100
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
7- Numerical Results – K locally 7- Numerical Results – K locally monitored machinesmonitored machinesCASES E tot E eff Yield N1 N2
Sim. 0.64898 0.35825 0.55202 2.75398 2.2599 An. 0.64605 0.35652 0.551846 2.75398 2.2599 1
Err % 0.45194 0.48318 0.03152 1.3770 0.7390 Sim. 0.47543 0.24270 0.51049 3.4071 1.2432 An. 0.47651 0.24265 0.509222 3.41109 1.2308 2
Err % 0.22737 0.02060 0.24839 0.0998 0.3110 Sim. 0.5748 0.5567 0.9686 19.302 11.706 An. 0.5753 0.5574 0.9687 19.71 11.782 3
Err % 0.086 0.125 0.01 1.63 0.304 Sim. 0.0273 0.0269 0.9866 3.443 0.344 An. 0.0271 0.0268 0.9868 3.414 0.313 4
Err % 0.732 0.37 0.02 0.116 0.124
3 machine cases
CASES E tot E eff Yield N1 N2 N3 N4 N5 N6 N7 N8 N9 Sim. 0.5522 0.0849 0.1538 2.892 2.604 2.381 2.184 1.997 1.809 1.616 1.393 1.106 An. 0.5559 0.0854 0.1538 2.9 2.618 2.317 2.179 2 1.82 1.682 1.381 1.099 1
Err% 0.67 0.58 0 0.2 0.35 1.6 0.125 0.075 0.275 1.65 0.3 0.175 Sim. 0.8025 0.4566 0.569 4.035 3.650 3.401 3.188 2.990 2.785 2.584 2.336 1.951 An. 0.8062 0.4588 0.5692 4.048 3.648 3.357 3.189 2.999 2.81 2.642 2.351 1.951 2
Err% 0.46 0.481 0.035 0.21 0.033 0.73 0.016 0.15 0.416 0.96 0.25 0
10 machine cases
System Yield Total E Effective E Buffer level Average 0.123 0.672 0.723 0.799
<1% 98 93 92 90 <2% 100 100 100 100
Summary of results
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
7- System Behavior7- System BehaviorTotal Throughput and System yield vs. N
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
3 5 7 9 11 13 15 17 19 21 23 25 27 29
N
Total throughput
System Yield
Effective throughput vs. N
0.485
0.49
0.495
0.5
0.505
0.51
0.515
0.52
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
N
EE
FF
h=3 Effective throughput vs. N
0.465
0.47
0.475
0.48
0.485
0.49
0.495
0.5
0.505
0.51
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
N
EE
FF
h=5
Effective throughput vs. N
0.515
0.52
0.525
0.53
0.535
0.54
0.545
0.55
0.555
0.56
0.565
3 5 7 9 11 13 15 17 19 21 23 25 27 29
N
EE
FF
h=0 - 100% insp
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
8- Conclusion and Future Research8- Conclusion and Future Research
- Quality issues and productivity aspects must be jointly considered in the design phase of production systems, since their correlation is evident.
-The proposed method paves the way to the integrated analysis and solution of other system design problem such as:
- Optimal design of control chart parameters;
- Optimal allocation of inspection devices;
- Optimal allocation of buffer space.
- New improvement of the method will be the integration of various scrap and rework policies in order to identify the optimal scrap/rework parameters.
- The proposed method, dealing with the interaction between SPC theory principles and production system design issues, provides accurate results in the performance analysis of such systems.
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
Thank you for your attention.
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >
10- System Behavior10- System Behavior
Effective throughput vs. N
0.515
0.52
0.525
0.53
0.535
0.54
0.545
0.55
0.555
0.56
0.565
3 5 7 9 11 13 15 17 19 21 23 25 27 29
N
EE
FF
Total Throughput and System yield vs. N
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
3 5 7 9 11 13 15 17 19 21 23 25 27 29
N
Total throughput
System Yield
piquality ri
qua lity rifalse pi ri iWi iOi hi(Ci,i) mi(Ci,i) i(Ci,i) i(Ci,i)
0.08 0.5 0.94 0.1 0.5 0.03 0.9 0 1 0.0027 0.6 0.1 0.47
The behavior of systems in which the first machine is monitored by the second one have been observed.
Dipartimento di Meccanica
Sezione Tecnologie Meccaniche e Produzione< Impact of SPC on System Performance >< Impact of SPC on System Performance >