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March 20, 2006 © Six Sigma Professionals, Inc.
Six Sigma Professionals, Inc.
Product & Process D
esign For 6 Sigma
©
ΣΣ
The Application of Axiomatic Design in DFSS:
A New Paradigm
by Dr. Basem Haik
WCBF’s 2nd Design for Six Sigma ConferenceSeptember 13-14, 2006
Four Season Hotel, Las Vegas
March 20, 2006 © Six Sigma Professionals, Inc.
Six Sigma Professionals, Inc.
Product & Process D
esign For 6 Sigma
©
ΣΣ
For more information about Six Sigma Professionals, Inc. (SSPI)
Please visit:www.SixSigmaPI.com Or email us @: info@SixSigmaPI.com Or call us @ (866) 642-8683
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
DFSS is a philosophy and a methodology that provides businesses with perspectives and tools to achieve new levels of performance both in service and product industries. Axiomatic design technology is a process to improve the quality and performance of complex system and product development. This process provides a systematic and logical methodology for deriving, documenting and optimizing designs. Design architectures resulting from axiomatic analysis provide frameworks for implementation planning, risk assessment, risk mitigation and robust design analysis. This session will give you practical insight into Axiomatic Design employment in Design for Six Sigma on the technical and deployment fronts. The key areas of focus are:
A high-level overview of Axiomatic DesignAxiomatic Design innovation and its synergy with TRIZA principle-based Design for Six Sigma using Axiomatic Design technologyDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
The key areas of focus are:A high-level overview of Axiomatic DesignA principle-based Design for Six Sigma using Axiomatic Design technologyAxiomatic Design innovation and its synergy with TRIZDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
The key areas of focus are:A high-level overview of Axiomatic DesignA principle-based Design for Six Sigma using Axiomatic Design technologyAxiomatic Design innovation and its synergy with TRIZDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
Axiom 1: The Independence AxiomA good design comprises of Design Parameters (DPs) that maintain the independence of functional requirements (FRs)
Design is a continuous mapping activity between 4 domains: CAs FRs DPs PVsSeveral corollaries and theorems were derived from this axiom.
Violation of
Axiom 1
Maximize Independence3
March 20, 2006
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esign For 6 Sigma
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Example of Independence Axiom: Water Faucet
• FR1:Control the flow of water• FR2: Control the temperature of
water
• DP1:Angle of valve 1, φ1• DP2: Angle of valve 2, φ2
Functional Requirements Design Parameters
φ2
φ1
Hot water Cold water
φ1
φ2
Hot water Cold water
Which Design is Independent?
3
March 20, 2006
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3The Principle of Independence Axiom
Mathematically*
22
12
AA
21
11
AA
⎦
⎤⎥
⎣
⎡⎢=
⎭⎩
⎫⎧⎬⎨
Functional Requirement 1
Functional Requirement 2 ⎭
⎫⎬
⎩
⎧⎨
Design Parameter 1
Design Parameter 2
* FRs and DPs are design vectors…
=Application
⎦
⎤⎥
⎣
⎡⎢
Inter-dependenciesOff-Diagonal
Elements⎭⎩
⎫⎧⎬⎨
Control the Flow
Control the temperature ⎩
⎧
⎭
⎫⎬⎨
Valve #1
Valve #2
Don’t Live With Coupling…Resolve IT.
March 20, 2006
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3
Problems With Coupled DesignLow quality and reliability in particular with bigger design matrices and several hierarchal levels
Customer usage and manufacturing variations (noise factors) usually win with coupled designs…Usually due to the ignorance of design mappings and coupling vulnerability.Optimization and variability reduction (even with aggressive Six Sigma) is at best a trade-off among functional requirements to achieve reasonable overall design…Remember the EXCEL Example.
Inherently a “weak” design because of conflicting objective due to design parameters. By definition, functions are independent to each others and only a poor selection of DPs creates dependencies.
Design improvement should be directed to “Uncouple” or “Decouple” the design where optimization of a function will not affect other functions.
March 20, 2006
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3Design Categories According to Axiomatic Design
⎭⎬⎫
⎩⎨⎧⎥⎦
⎤⎢⎣
⎡=⎭⎬⎫
⎩⎨⎧
21
00
21
22
11
DPDP
AA
FRFR
Uncoupled Design
⎭⎬⎫
⎩⎨⎧⎥⎦
⎤⎢⎣=⎭⎬⎫
⎩⎨⎧
Valve #2
Valve #1Control the Temperature
Control the Flow ⎡
Off-Diagonal Interdependencies are Zeros —means there is no relationship between the FR and the corresponding DP
FR1 = A11DP1 + 0FR2 = 0 +A22DP2
Independent Design is the BEST!
March 20, 2006 © Six Sigma Professionals, Inc.
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esign For 6 Sigma
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3
What Is The Other Design Category?
March 20, 2006
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esign For 6 Sigma
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Design Categories According to Axiomatic Design3
⎭⎬⎫
⎩⎨⎧⎥⎦
⎤⎢⎣
⎡=⎭⎬⎫
⎩⎨⎧
210
21
2221
11
DPDP
AAA
FRFR
Decoupled Design
⎭⎬⎫
⎩⎨⎧⎥⎦
⎤⎢⎣=⎭⎬⎫
⎩⎨⎧
Valve #2
Valve #1Control the Temperature
Control the Flow ⎡
FR1 = A11DP1FR2 = A21DP1 + A22 DP2
Satisfying Axiom 1 but needs proper sequencing for design optimization!
Sequence: Design DP1 for FR1 then Use DP2 for FR2
Design According to the Sequence !!!
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Coupling Vector Representation
FR1
FR2
DP1
DP2
(1)
(2)
Coupled DesignSequence Dependent
FR1 DP1
FR2 DP2=
Full Matrix[ ]
FR1
FR2
(1)
(2)
DP1
DP2
Decoupled DesignSequence Dependent
FR1 DP1
FR2 DP2=
Triangular Matrix [ ]
FR1
FR2
DP1
DP2
(1)
(2)
Uncoupled DesignSequence Independent
FR1 DP1
FR2 DP2=
Diagonal Matrix [ ]
3
Don’t Live With Coupling…Resolve IT.
March 20, 2006
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esign For 6 Sigma
© Six Sigma Professionals, Inc.©
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Systems Design the DFSS Way
1
{CAs}...
Customer Domain
{FRs}...
Functional Domain
{DPs}...
Physical Domain
{PVs}...
Process Domain
mapping mapping mapping
CustomerAttributes
(CAs)
Functional Requirements
(FRs)
DesignParameters
(DPs)
ProcessVariables
(PVs) 2 ...
What
.
.
.
How
mapping
Design Hierarchy
.
.
.
What
.
.
.
How
mapping
Process designProduct design
3
{CAs}...
Customer Domain
Functional Domain
Physical Domain
Process Domain
mapping mapping mapping
CustomerAttributes
(CAs)
Functional Requirements
(FRs)
DesignParameters
(DPs)
ProcessVariables
(PVs)
FR1
FR11 FR12
FR1
FR11 FR12
FR1
FR11 FR12
The Independence AxiomA good design comprises of Design Parameters (DPs) that maintain the independence of functional requirements (FRs)Also between DPs and PVs.
4
Applying Design Principles
March 20, 2006
Six Sigma Professionals, Inc.
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esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
The key areas of focus are:A high-level overview of Axiomatic DesignA principle-based Design for Six Sigma using Axiomatic Design technologyAxiomatic Design innovation and its synergy with TRIZDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
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Principle-based DFSSIdentification of key design principles as the foundation of the DFSS process.
Customer (user) driven design requirementsEstablish knowledge of performance variationMaximize independenceMinimize complexityConceptual superiorityOptimize function in the presence of noiseVerify that optimization translates to meeting user requirements
1234567
March 20, 2006
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Principle-based DFSS Techniques
Axiomatic Design
Robust Design Methods
Lean Manufacturing Principles
Theory of Inventive Problem Solving
(TIPS/TRIZ)
Principle-based DFSS (ICOV)
Identify ValidateConceptualize Optimize
Stag
e 1:
Id
ea C
reat
ion
Stag
e 2:
V
OC
& V
OB
Stag
e 3:
C
once
pt
Dev
elop
men
t
Stag
e 4:
Pr
elim
inar
y D
esig
n
Tollg
ate
1
Tollg
ate
2
Tollg
ate
3
Tollg
ate
4
Stag
e 5:
O
ptim
izat
ion
Tollg
ate
5
Stag
e 6:
V
erif
icat
ion
Tollg
ate
6
Stag
e 7:
La
unch
R
eadi
ness
Tollg
ate
7
Prod
uctio
n
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
The key areas of focus are:A high-level overview of Axiomatic DesignA principle-based Design for Six Sigma using Axiomatic Design technologyAxiomatic Design innovation and its synergy with TRIZDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
Relationship to TRIZ & Creativity Tools
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎪⎪⎪
⎭
⎪⎪⎪
⎬
⎫
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
mDP
DPDPDP
XXXXXX
XXX
XXX
mFR
FRFRFR
1:131211
:...0
1:
131211
FR1.1 FR1.2
FR1 FR2
FR
FunctionalDomain
DP1.1 DP1.2
DP1 DP2
DP
Physical Domain
Physical Mapping: Map FRs to Design Parameters (DPs)
Axi
omat
ic D
esig
n Zi
gzag
ging
Met
hod
Zigzagging
TRIZ Opportunity, Benchmarking, Best Practices, Brainstorming, Pain storming, Assumption Busting, etc.
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
The Application of Axiomatic Design in DFSS: A New Paradigm
The key areas of focus are:A high-level overview of Axiomatic DesignA principle-based Design for Six Sigma using Axiomatic Design technologyAxiomatic Design innovation and its synergy with TRIZDesign for Lean Six Sigma: An axiomatic design application to cellular manufacturing
March 20, 2006
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•Case Study: Principle-based Cellular Lean Design
Objective: transform traditional production system from process orientation to cellular orientation using DFSS principle (3): Maximize Independence. A feedback mechanism for continuous improvement is also suggested for evaluating and improving the cellular design against pre-selected performance criteria The needs of plant are to get flexibility ∆:
More product varietySmaller batch sizesHighest quality and more frequent deliveriesLower production costSpeed and ability to respond to changing needs
Design of cellular manufacturing system based on AD principles
Design of cellular manufacturing system based on AD principles
Implementation of cellular design
Implementation of cellular design
Performance evaluation of key metrics
Performance evaluation of key metrics
Targets met?
AD based continuous improvement process
AD based continuous improvement process
Improvement of the cellular system
Improvement of the cellular system
Set improved targetsSet improved targets
No
Yes
Preliminary Design Stage
Preliminary Design Stage
Design of cellular manufacturing system based on AD principles
Design of cellular manufacturing system based on DFSS principles
Implementation of cellular design
Implementation of cellular design
Performance evaluation of key metrics
Performance evaluation of key metrics
Targets met?
AD based continuous improvement process
DFSS based continuous improvement process
Improvement of the cellular system
Improvement of the cellular system
Set improved targetsSet improved targets
No
Yes
Preliminary Design Stage
Preliminary Design Stage
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
DP = Cellular Manufacturing System Design
FR = Provide a flexible production in line with customer needs
This case study was conducted at a company manufacturing aluminum walkways, bridges, stairs and ramps in Florida.
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Hierarchical Level 2 Analysis
FR1=Classify and group products/ components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
FR = Provide a flexible production in line with customer needs
DP = Cellular Manufacturing System Design
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Applying Principle-based System Design: Hierarchical Level 2 Design Matrix
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
4321
000000
4321
DPDPDPDP
XXXXXXX
XXX
FRFRFRFR
March 20, 2006
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© Six Sigma Professionals, Inc.©
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Applying Principle-based System Design: Hierarchical Level 2 Analysis
FR1=Classify and group products/components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
DP = Cellular Manufacturing System
Design
Legend
‘X’ : a strong relationship‘0’ : absence of such relationship.
Conclusion: The design is decoupled, and thus, satisfies Axiom 1.
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Hierarchical Level 3 Analysis: For FR1(=Classify and group products/ components for simple material flow) with DP1 (=Procedure for defining product families) in mind:
FR11 = Determine high volume products/ components to group
FR12 = Determine operations and machine types for producing each product family
FR13 = Form product families
FR14 = Determine final number of machine groups
DP11 = Product-Quantity Pareto Analysis
DP12 = Machine-Component Incidence Matrix
DP13 = Products grouping techniques
DP14 = Cost Analysis and economic justification techniques
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Applying Principle-based System Design: Hierarchical Level 3 Analysis (FR1)
FR11 = Determine high volume products/ components to group
FR12 = Determine operations and machine types for producing each product family
FR13 = Form product families
FR14 = Determine final number of machine groups
DP11 = Product-Quantity Pareto Analysis
DP12 = Machine-Component Incidence Matrix
DP13 = Products grouping techniques
DP14 = Cost Analysis and economic justification techniques
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
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Applying Principle-based System Design: Hierarchical Level 3 Design Matrix (FR1)
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Hierarchical Level 2 Analysis
FR1=Classify and group products/ components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
FR = Provide a flexible production in line with customer needs
DP = Cellular Manufacturing System Design
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
14131211
00000000
14131211
DPDPDPDP
XXXXX
XXX
FRFRFRFR
Conclusion: The design is decoupled, and thus, satisfies Axiom 1.
March 20, 2006
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In Plain English…The sequence of activities revealed by the design matrix is as
follows:1.Establish the high volume products through Product-Quantity
(Pareto) analysis (DP11), then…2.Group similar products (in terms of their process
requirements) into product families (DP12), then…There are several algorithmic procedures to accomplish this task. Most of them use the Machine-Component Incidence Matrix. These algorithms swap rows and the columns of this matrix until suitable block-diagonal sub-matrices or near block-diagonal sub-matrices are obtained. The products that fall into the same sub-matrix are candidates to be allocated to a potential cell.
3.Decide on how many of these cells to implement based on economic justification principles (DP13), then…
4.Perform cost benefit analyses on each potential cell formation. In this process, each candidate cell’s contribution to the company’s bottom line in terms of productivity, lead time and profitability together with return on investment are calculated.Those cells that satisfy the company internal rate of return arerecommended for formation (DP14) .
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Hierarchical Level 3 Analysis: For FR2(=Define production strategy based on product specifications with DP2 (=Procedure for selecting production strategy) in mind:
FR21=Determine the master process
FR22=Select most appropriate process elements
FR23=Determine required training/ education needs
FR24=Motivate labor participations
DP21=Master Process selection
DP22=Production resources selection procedure
DP23=Multi-purpose labor training programs
DP24=Gain sharing program
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Hierarchical Level 2 Analysis
FR1=Classify and group products/ components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
March 20, 2006
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Process D
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
FR = Provide a flexible production in line with customer needs
DP = Cellular Manufacturing System Design
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Applying Principle-based System Design: Hierarchical Level 3 Design Matrix (FR2)
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Hierarchical Level 2 Analysis
FR1=Classify and group products/ components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
March 20, 2006
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
FR = Provide a flexible production in line with customer needs
DP = Cellular Manufacturing System Design
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
24232221
00000000
24232221
DPDPDPDP
XXXXX
XXX
FRFRFRFR
Conclusion: The design is decoupled, and thus, satisfies Axiom 1.
March 20, 2006
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In plain English…
The sequence revealed by the design matrix is as follows:
1.Establish the master process based on product specifications (DP21), then…
2.Determine the production resources (DP22), then…
3.Complete the resource selection (DP23), then…
4.The education and training requirements of the workers can be established (DP24).
For ensuring the full participation of workers in the education and training activities followed by transition to cellular manufacturing, appropriate gain sharing programs must be established and announced to the workers for strong buy in.
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Hierarchical Level 3 Analysis: For FR3 (= Rearrange resources to minimize waste) with DP3 (=Product oriented layout) in mind:
FR31=Minimize material handling
FR32=Eliminate wasted motion of operators
FR33=Minimize waste due to imbalance in the system
DP31= Material flow oriented layout
DP32 =Arrangement of stations to facilitate operator tasks
DP33 =Balanced resources in response to Takt time (Takttime=Available Time /Demand)
DP24=Gain sharing program
March 20, 2006
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Hierarchical Level 2 Analysis
FR1=Classify and group products/ components for simple material flow
FR2=Define production strategy based on product specifications
FR3=Rearrange resources to minimize waste
FR4=Provide means to control production based on customer demand
DP1=Procedure for defining product families
DP2=Procedure for selecting production strategy
DP3=Product oriented layout
DP4=Pull production control system
March 20, 2006
Six Sigma Professionals, Inc.
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Process D
esign For 6 Sigm
a
© Six Sigma Professionals, Inc.©
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Applying Principle-based System Design: Hierarchical Level 1 Analysis
FR = Provide a flexible production in line with customer needs
DP = Cellular Manufacturing System Design
32
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Partial Zigzagging Tree…
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
4321
*
4321
DPDPDPDP
XXXXXXX
XXX
FRFRFRFR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
14131211
*
00
14131211
DPDPDPDP
XXXXX
XXX
FRFRFRFR
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
24232221
*
00
24232221
DPDPDPDP
XXXXX
XXX
FRFRFRFR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
333231
*333231
DPDPDP
XXXXX
X
FRFRFR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
434241
*434241
DPDPDP
XXXXX
X
FRFRFR
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
=
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
225224223222221
*
000
225224223222221
DPDPDPDPDP
XXXXXX
XXXXX
X
FRFRFRFRFR
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡232231
*232231
DPDP
XXX
FRFR ⎥
⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡242241
*242241
DPDP
XXX
FRFR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
323322321
*00
0323322321
DPDPDP
XX
X
FRFRFR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
333332331
*00
0333332331
DPDPDP
XX
X
FRFRFR⎥
⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
413412411
*413412411
DPDPDP
XXXXX
X
FRFRFR
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
423422421
*0423
422421
DPDPDP
XXXX
X
FRFRFR
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡432431
*432431
DPDP
XXX
FRFR
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡42124211
*42124211
DPDP
XXX
FRFR
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡=⎥
⎦
⎤⎢⎣
⎡42224221
*42224221
DPDP
XXX
FRFR
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
Results
Metric Before the study
After the study
Raw matl. stock (days of inv.)
11 3.5
Lead Time (days) 18 7
Scrap Rate (percentage)
3 1.6
Throughput (units pairs)
50 70
Overtime (hours/week)
300 60
WIP (days inventory)
6 2.5
March 20, 2006
Six Sigma Professionals, Inc.
Product, Service & Process D
esign For 6 Sigma
© Six Sigma Professionals, Inc.©
ΣΣ
Questions?
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