dfss knowledge management repetition process

March 20, 2006 © Six Sigma Professionals, Inc.

Six Sigma Professionals, Inc.

Product & Process D

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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



Product & Process D

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For more information about Six Sigma Professionals, Inc. (SSPI)

Please visit:www.SixSigmaPI.com Or email us @: [email protected] Or call us @ (866) 642-8683

http://www.sixsigmapro.com/

mailto:[email protected]

March 20, 2006


Product, Service & Process D

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© Six Sigma Professionals, Inc.©

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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

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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

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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

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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

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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.

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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.

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3Design Categories According to Axiomatic Design

⎭⎬⎫

⎩⎨⎧⎥⎦

⎤⎢⎣

⎡=⎭⎬⎫

⎩⎨⎧

21

00

21

22

11

DPDP

AA

FRFR

Uncoupled Design

⎭⎬⎫

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⎩⎨⎧

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!



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3

What Is The Other Design Category?

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Design Categories According to Axiomatic Design3

⎭⎬⎫

⎩⎨⎧⎥⎦

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210

21

2221

11

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AAA

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Decoupled Design

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⎩⎨⎧

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.

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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

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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

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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

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Stag

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2

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3

Tollg

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Stag

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ptim

izat

ion

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ate

5

Stag

e 6:

V

erif

icat

ion

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ate

6

Stag

e 7:

La

unch

R

eadi

ness

Tollg

ate

7

Prod

uctio

n

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Relationship to TRIZ & Creativity Tools

⎪⎪⎪

⎭

⎪⎪⎪

⎬

⎫

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FRFRFR

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:...0

1:

131211

FR1.1 FR1.2

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FR

FunctionalDomain

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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.

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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


Implementation of cellular design


Performance evaluation of key metrics


Targets met?

AD based continuous improvement process


Improvement of the cellular system


Set improved targetsSet improved targets

No

Yes

Preliminary Design Stage



Design of cellular manufacturing system based on DFSS principles





Targets met?


DFSS based continuous improvement process



Set improved targetsSet improved targets

No

Yes



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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 2 Design Matrix

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⎧

4321

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FR1=Classify and group products/components for simple material flow








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





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Applying Principle-based System Design: Hierarchical Level 3 Design Matrix (FR1)

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⎪⎪⎭

⎪⎪⎬

⎫

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14131211

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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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Applying Principle-based System Design: Hierarchical Level 3 Design Matrix (FR2)

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⎪⎪⎭

⎪⎪⎬

⎫

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⎣

⎡

=

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⎧

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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

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Partial Zigzagging Tree…

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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

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Questions?

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