VECTOR Detail Design: The Application of Axiomatic Design

Integration of VECTOR & Next-Generation DfLSS

for Fast Innovation within ARDEC

VECTOR Detail Design: The Application of

Axiomatic Design

Dr. Basem Haik, President

Six Sigma Professionals, Inc. (SSPI)

Confidential © 2005 Six Sigma Professionals, Inc. (SSPI) . All Rights Reserved. 1

[email protected]

(734) 765-5229

Dr. Basem Haik

• President, Six Sigma

Professionals, Inc. (SSPI)

• Web: www.SixSigmaPI.com

• Mail:

Six Sigma Professionals, Inc. (SSPI)

39505 Dorchester Circle

Canton, Michigan 48188 USA

• Email:


Professionals, Inc. (SSPI)

• Background: Ph.D. (WSU)&

Doctor of Manfg. (UOM), 20 yrs in

Prod. Dev./RD, Tech. Specialist @

Ford, SSPI President

• Experience / Key Clients:

Cessna, Bell Helicopter, Baxter,

GM, Textron Systems, …

• 6 Authored DFSS Texts (+ 2

forthcoming + many papers)

• Email:

[email protected]

• Tel.: (734) 765-5229 (USA)

• Fax: (734) 728-8507 (USA)

Objective

• Introduce Axiomatic Design Methodology (HL Intro)

• Explain how Axiomatic Design was used in Vector

Detail Design phase

• Demystify the linkages to Computer-Aided DFSS


What is an “AXIOM”?

• An “axiom”, in mathematics and logic, is a general

statement accepted without proof as the basis for logically

deducing other statements (e.g. corollaries and theorems),

which later form a logical system of its own.

• Axioms widely used are those related to engineering and


• Axioms widely used are those related to engineering and

mathematical operations– Newton laws - Archimedes' Axiom - Euclidean geometry

– Thermodynamics - Field Axiom

– Probability Axioms (e.g. the associative law and the commutative law of set

theory)

An axiom , a postulate, is a self-evident statement without proof, but the truth of the statement need not be readily evident.

What is an “AXIOM”? (cont’d)

• An axiomatic system is valid and sustained if the set

of axioms satisfy the following attributes:

– The set of axioms are independent; i.e., no one axiom

statement may be deduced from any combination of the

others.


others.

– The axioms are consistent, i.e., it is not possible to

deduce contradictory theories and corollaries from them.

– The axiomatic set is complete; i.e., any true statement

within the system may be deduced from the axioms.

Axiomatic System Example: Newton’s Laws

• Newton LAW I.

– Every body perseveres in its state of rest, or of uniform

motion in a right line, unless it is compelled to change that

state by forces impressed thereon.

• Newton LAW II.

– The alteration of motion is ever proportional to the motive


– The alteration of motion is ever proportional to the motive

force impressed; and is made in the direction of the right

line in which that force is impressed.

• Newton LAW III.

– To every action there is always opposed an equal reaction;

or the mutual actions of two bodies upon each other are

always equal, and directed to contrary parts.

Axiomatic System Example: Laws of

Thermodynamics

• First law

– In any process, the total energy of the universe remains the same

OR

– for a thermodynamic cycle the sum of net heat supplied to the

system and the net work done by the system is equal to zero.


• Second law

– The entropy of an isolated system not in equilibrium will tend to

increase over time, approaching a maximum value at equilibrium.

• Third law

– As temperature approaches absolute zero, the entropy of a

system approaches a constant minimum.

Axiomatic System Example: Laws of

Thermodynamics

• First law

– In any process, the total energy of the universe remains the same

OR

– for a thermodynamic cycle the sum of net heat supplied to the

system and the net work done by the system is equal to zero.


• Second law

– The entropy of an isolated system not in equilibrium will tend to

increase over time, approaching a maximum value at equilibrium.

• Third law

– As temperature approaches absolute zero, the entropy of a

system approaches a constant minimum.

Axiomatic System Example: Euclidean

Geometry (cont’d)

• Euclidean geometry is an axiomatic system, in which all theorems

("true statements") are derived from a finite number of axioms. Near

the beginning of the first book of the Elements, Euclid gives five

postulates (axioms):

1. Any two points can be joined by a straight line.

2. Any straight line segment can be extended indefinitely in a straight line.


2. Any straight line segment can be extended indefinitely in a straight line.

3. Given any straight line segment, a circle can be drawn having the segment

as radius and one endpoint as center.

4. All right angles are congruent.

5. Parallel postulate. If two lines intersect a third in such a way that the sum of

the inner angles on one side is less than two right angles, then the two lines

inevitably must intersect each other on that side if extended far enough.

Axiomatic System Example: Field

Axioms

• A field is a set F with binary operations + ("plus") and . ("times") that obey the

following axioms:

– Law of closure: If a; b belong to F then a + b and a . b (or ab = a . b ) are both in F.

– Commutative Law: If a; b belong to F then a + b = b + a and a . b = b . a.

– Associative Law: If a; b; c belong to F then a + (b + c) = (a + b) + c and a . (b . c) = (a

. b) . c.

– Distributive Law: If a; b; c belong to F then a(b + c) = ab + ac.


– Distributive Law: If a; b; c belong to F then a(b + c) = ab + ac.

– Existence of identities: There exist distinct elements (denoted by) 0 and 1 in F such

that for every a belong to F: 0 + a = a and 1 . a = a. We call 0 and 1 the additive identity

and the multiplicative identity, respectively.

– Existence of inverses: • Additive inverse: If a belongs to F then there exists an element b belong to F such that b + a = 0 (we call b

an additive inverse of a.)

• Multiplicative inverse: If a belongs to F and a ≠ 0 then there exists an element b belongs to F such that b.a

= 1 (we call b a multiplicative inverse of a.)

What Is Axiomatic Design?

• Axiomatic Design (AD) is a general principle for design analysis and

design synthesis developed by Prof. Nam P. Suh of MIT.

Axioms are general principles or self-evident truths that cannot be derived or proven to be true except that there are no counter-examples or exceptions to

prove otherwise.


“ The goal of axiomatic design is many fold: to make human designers

more creative, reduce the random search process, minimize the

iterative trial and error process, and determine the best design

among those proposed.”

Prof. Nam Suh

Designer Psychological Inertia

Current Practice:

• Novel ideas in engineering and business are mostly produced by the trial-and-error method.

• No rules for systematic solution generation, and the process is often stochastic.

• If an idea is weak initially, it is discarded, and a new idea is suggested.

• The flow of ideas is uncontrollable, and


• The flow of ideas is uncontrollable, and attempts (trials) are repeated as many times as needed to find a solution.

• Psychological inertia sources:

• Perceptual (stereo-typing)

• Cultural (taboos, tradition)

• Emotional (fear of change)

• Environmental (autocratic supervisors)

• Intellectual/Expressive

Although seemingly random, most trials have a common attribute: they are more numerous along a so-called vector of psychological inertia.

Axiomatic Design

• Axiom 1: The Independence Axiom

– A good design comprises of Design Parameters (DPs) that maintain the

independence of functional requirements (FRs)

• Axiom 2: The Information Axiom

– Among the designs that satisfy Independence Axiom, the best design is

one that requires the least amount of “information” to achieve the design

goal.

Violation of

Axiom 1

Violation of

Axiom 2


• Over 40 corollaries and theorems were derived from these two axioms.

Conceptual Quality

Do we have the RIGHT concept?

OperationalQuality

Do we develop the concept RIGHT?+

Axiomatic Design develops CONCEPTUAL & OPERATIONAL IMMUNITY

Axiom1 Axiom2

Axiomatic Design (cont’d)

FR1: Control the flow of water

FR2: Control the temperature of waterDP1:Angle of valve 1

DP2: Angle of valve 2

Functional Requirements Design Parameters

Hot water Cold water Hot water Cold water


Hot water Cold water Hot water Cold water

Source: El-Haik, B., “Axiomatic Quality & Reliability”, John Wiley & Sons, Inc., New York, April, 2005.

DP2

DP1 DP2

DP1

Example of Independence Axiom: Example of Independence Axiom: Example of Independence Axiom: Example of Independence Axiom:

Water FaucetWater FaucetWater FaucetWater Faucet

DP2

DP1

Hot water Cold water

DP2

Hot water Cold water


DP1

××××

=

==

2

1

eTemperaturControl FR2

FlowControl FR1

DP

DP

Coupled Design(DPs create conflicting functions)

Uncoupled Design(DPs maintain independence of functions)

××

=

==

2

1

0

0

eTemperaturControl FR2

FlowControl FR1

DP

DP

Example of Independence Axiom:

Water Faucet (cont’d)

DP2222DP1111

Hot water Cold waterIn E

l-Ha

ik, B

., “Axio

ma

tic Qu

ality

& R

elia

bility

”, Joh

n W

iley

& S

on

s, Inc., N

ew

Yo

rk, A

pril,

20

05

.


Coupled Design(DP’s create conflicting functions)

=

2

1

2

1

DP

DP

X

X

FR

FR

Violation of

Axiom 1

Ha

ik, B

., “Axio

ma

tic Qu

ality

& R

elia

bility

”, Joh

n W

iley

& S

on

s, Inc., N

ew

Yo

rk, A

pril,

20

05

.

Coupling is BAD!

X

X

Corollary No. 3: : Beverage can design

matrix

FR1= Need to fill can

FR2= Need to seal can

FR3= Need to re -

DP1= Open top drawn container

DP2= Cold welded lid

DP3= Tear away


FR3= Need to re -open can

DP3= Tear away strip in lid

=

3

2

1

3

2

1

33

21

11

DP

DP

DP

A

A

A

FR

FR

FR

0

0

Auto Lift Gate Design Example

Structural Rigidity A11 0 0 0 0 0 Mass, Geometry, Moment of Inertia

Easy to Open A21 A22 A23 0 0 0 Gate Strut, Hinge

Easy to Close = A31 A32 A33 0 0 0 Gravity, Hinge

Seal 0 A42 0 A44 0 0 Weather-strip, Seal gap

Stay Latched 0 0 0 0 A55 0 Latch strength, friction

Low Closing Speed 0 A62 0 A64 A65 A66 Airbinding


Nayak, R., Im, K.H., Lin, C.L., and Kapadnis, P. (2002) “Robust design of liftgate opening/closing efforts,”

Int. Journal of Materials & Product Technology, Vol 17, Nos. 5/6, pp.368-374.

FR1

FR2

DP1

DP2

(1)

(2)

FR1

FR2

(1)

(2)

DP1

DP2

FR1

FR2

DP1

DP2

(1)

(2)

Coupling Vector Representation


Coupled DesignSequence Dependent

FR1 DP1

FR2 DP2=

Full Matrix[ ]

FR1

Decoupled DesignSequence Dependent

FR1 DP1

FR2 DP2=

Triangular Matrix [ ]

FR1

Uncoupled DesignSequence Independent

FR1 DP1

FR2 DP2=

Diagonal Matrix [ ]

Coupling Could Happens Across Design Hierarchy

Independence of Functional

Requirements

Uncoupled Decoupled Coupled

=

3

2

1

00

00

00

3

2

1

DP

DP

DP

X

X

X

FR

FR

FR

=

3

2

1

0

00

3

2

1

DP

DP

DP

XXX

XX

X

FR

FR

FR

=

3

2

10

3

2

1

DP

DP

DP

XXX

XXX

XX

FR

FR

FR


More Ideal Less Ideal

• A is non-zero quantity, signifying the fact that there is a strong relationship between FR and the

corresponding DP

• 0 means there is no relationship between them

Axiom1: Design Analysis

• FR1: Freeze food for long-term

preservation

• FR2: Maintain food at cold

temperature for short-term

preservation

• DP1: Freezer section

• DP2: Refrigerator section

• DP11: Turn on and off the compressor

Zig

Zig

Zag

Zag

Lev

el 1


• FR11: Control the temperature of the

freezer in the range - 18 C

• FR12:Maintain uniform temperature at

preset temperature

• FR13: Control humidity to relative

humidity 50%

• DP11: Turn on and off the compressor

when the air temperature is higher

and lower that the set temperature

• DP12: Blow the air into the freezer

section and circulate it uniformly

throughout the freezer section at all

times

• DP13: Condense the moisture in the

returned air when its dew point is

exceeded

Zig

Zig

Zig

Lev

el 2


VECTOR Design Hierarchy Using Axiomatic Design

Zigzagging Process

.

.

.

Deliverables

.

.

.

Major Activities

Zigg mapping

VECTOR Design process is a mapping from What to How Domains

Zig-zagging

What How


What How

Zigg mapping Zigzagging is a team activity

Sub-Deliverables Tasks/Activities


VECTOR Detail Design Steps

• Two major steps:

1. Zigzag VECTOR � Design mapping

1. Deliverables are mapped to major activities (Level 1 hierarchy)

and Sub-deliverables to tasks (Level 2 hierarchy)


2. Convert matrices to process maps

1. Find the sequence of activities that minimizes coupling and

thus scrap and rework

2. Sequence activities according to the matrix intended mapping

(black X )

Block 1: Level 1 Zigzagging

No. DPB1-2 DPB1-8 DPB1-1

DPB1-

5,DPB1-

6,DPB1-

7, DPB1-9

Est

ab

lish

In

teg

rate

d D

ata

En

vir

on

me

nt

(ID

E)

Ga

the

r &

Pro

cess

VO

C,

ide

nti

fy c

riti

cal

cust

om

er

ne

ed

s

Design Matrix: Level 1

[A]Relationship Meaning

X A required relationship

exist

X A coupling relationship

exist


No. Deliverables Major Activities

De

ve

lop

ov

era

ll,

inte

gra

ted

pro

ject

pla

n

Est

ab

lish

In

teg

rate

d D

ata

En

vir

on

me

nt

(ID

E)

Ga

the

r &

Pro

cess

VO

C,

ide

nti

fy c

riti

cal

cust

om

er

ne

ed

s

(Cu

sto

me

r C

en

tric

Pro

cess

)

Co

nta

rct

Aw

ard

ing

Pro

cess

FRB1-1 Project Plan X X X

FRB1-2 Major program assumptions X X X

FRB1-3 Ranked & Prioritized Critical Customer Needs X

FRB1-4 Awarded Contract(s) X

0 No relationship exist

Coupling

Problems With Coupled Design

• Coupling in VECTOR � Reworked and/or

scrapped activities and tasks… NOT Lean

• Inherently a “weak” design because of conflicting

requirements due to the selection or the design of VECTOR

procedures and processes.


procedures and processes.

• Optimization is at best a trade-off…

• IPT skills, experience and decision making may create

variation in implementation which will aggravates the

complexity of VECTOR.

Select/design/change Vector procedures to Uncouple/ Decouple Design

Design Precedence…

• The sequence of activities revealed by the design matrix will be developed by SSPI similar to the one below

DPB1-2: Contract

DPB1-1 : Gather & Process

VOC, identify critical

FR1: Awarded Contract(s)FR2: Ranked & Prioritized Critical Customer Needs No. DPB1-2 DPB1-8 DPB1-1

DPB1-

5,DPB1-

6,DPB1-

7, DPB1-9


De

ve

lop

ov

era

ll,

inte

gra

ted

pro

ject

pla

n

Est

ab

lish

In

teg

rate

d D

ata

En

vir

on

me

nt

(ID

E)

Ga

the

r &

Pro

cess

VO

C,

ide

nti

fy c

riti

cal

cust

om

er

ne

ed

s

Design Matrix: Level 1

[A]Relationship Meaning

X A required relationship

exist

X A coupling relationship

exist

0 No relationship exist

DPB1-8: Establish

FR3: Major program assumptions


DPB1-2: Contract

Awarding Process


customer needs (Customer

Centric Process)

Level 1 Level 1 Level 1 Level 1

MapMapMapMap


De

ve

lop

ov

era

ll,

inte

gra

ted

pro

ject

pla

n

Est

ab

lish

In

teg

rate

d D

ata

En

vir

on

me

nt

(ID

E)

Ga

the

r &

Pro

cess

VO

C,

ide

nti

fy c

riti

cal

cust

om

er

ne

ed

s

(Cu

sto

me

r C

en

tric

Pro

cess

)

Co

nta

rct

Aw

ard

ing

Pro

cess

FRB1-1 Project Plan X X X

FRB1-2 Major program assumptions X X X

FRB1-3 Ranked & Prioritized Critical Customer Needs X

FRB1-4 Awarded Contract(s) X

DPB1-8: Establish

Integrated Data

Environment (IDE)

DPB1-2: Develop overall,

integrated project plan

FR4: Project Plan

Apply Sequencing Algorithms ( EXCEL/Matlab macros)

Level 2

DPB1-4

DPB1-2 DPB1-2-1 DPB1-2-2 DPB1-2-3 DPB1-2-4

Ide

nti

fy s

kil

ls f

or

pro

ject

an

d f

orm

IP

T (

10

1)

CS

P P

roce

du

re

Pro

ject

Ch

art

er

AR

DE

C M

S P

roje

ct

Re

spo

nsi

bil

ity

[A]

.

.

.

Deliverables

.

.

.

Major Activities

Zigg mapping

What How

Zigg mapping

Zig-

zagging

What How


Develop overall,


FR4: Project Plan


Develop overall, integrated project plan Ide

nti

fy s

kil

ls f

or

pro

ject

an

d f

orm

IP

T (

10

1)

CS

P P

roce

du

re

Pro

ject

Ch

art

er

AR

DE

C M

S P

roje

ct

Te

mp

late

Re

spo

nsi

bil

ity

FRB1-2-1 ID Team Members X � Primary Responsibility

FRB1-2-2 Determine CSP X X � Secondary Responsibility

FRB1-2-3 Define Scope X X X

FRB1-2-4 Determine Precedence X X

SE

DE

Project Mngmnt PM

Logistics

Process Assurance (PA)

QESA

otherR =

Re

spo

nsi

ble

; S

=

can

be

Su

pp

ort

ive

; C

=

ha

s to

be

Co

nsu

lte

d;

I

= h

as

to b

e I

nfo

rme

d.

Coupling

VTB Block 1 w/o Common

DPB1-2: Contract

Awarding Process




Centric Process)

DPB1-8: Establish

Integrated Data

Environment (IDE)

DPB1-2: Develop

overall,

integrated project

plan

FR1: Awarded Contract(s) FR2: Ranked & Prioritized Critical Customer Needs


FR4: Project Plan

.

.

.

Deliverables

.

.

.

Major Activities

Zigg mapping

What How

Zigg mapping

Zig-

zagging

What How



DPB1-2:-1 Identify skills

For project and form

IPT (101)

FRB1-2-1: ID Team Members

DPB1-2-2 CSP

Procedure)

FRB1-2-2: Determine CSP

DPB1-2-3 Project

Charter

FRB1-2-3: Define Scope

DPB1-2-4 ARDEC MS

Project Template

FRB1-2-4: Determine Precedence

Level 2Level 2Level 2Level 2

MapMapMapMap

VTB Block 1 w/o Common (cont’d)

DPB1-8 DPB1-8-1 DPB1-8-2 DPB1-8-3

Giv

e I

PT

acc

ess

rig

hts

pro

ced

ure

(e

.g.

OC

S)-

(au

tom

ati

c/m

an

ua

l)

Re

spo

nsi

bil

ity

.

.

.

Deliverables

.

.

.

Major Activities

Zigg mapping

What How

Zigg mapping

Zig-

zagging

What How


Establish Integrated

Data Environment

(IDE)



Establish Integrated Data

Environment (IDE) Giv

e I

PT

acc

ess

rig

hts

On

lin

e t

oo

ls o

r a

pro

ced

ure

(e

.g.

OC

S)-

Au

tom

ati

c /M

an

ua

l

Ve

rsio

n c

on

tro

l

(au

tom

ati

c/m

an

ua

l)

Re

spo

nsi

bil

ity

FRB1-8-1 Access project data X � Primary Responsibility

FRB1-8-2 Share poject data X X � Secondary Responsibility

FRB1-8-3 Control project data X X X

SE

DE

Project Mngmnt PM

Logistics

Process Assurance (PA)

QESA

otherR =

Re

spo

nsi

ble

; S

=

can

be

Su

pp

ort

ive

; C

=

ha

s to

be

Co

nsu

lte

d;

I

Coupling


DPB1-8-1: Give IPT

access rights

DPB1-8-2 : Online tools or a

procedure (e.g. OCS)-

Automatic /Manual

DPB1-8-3: Version

control (

automatic/manual)

FRB1-8-1: Access project dataFRB1-8-2: hare project data

FRB1-8-3: Control project dataLevel 2Level 2Level 2Level 2

MapMapMapMap


DPB1-2: Contract

Awarding Process




Centric Process)


Data Environment

(IDE)

Develop overall,


FR1: Awarded Contract(s) FR2: Ranked & Prioritized Critical Customer Needs


FR4: Project Plan

.

.

.

Deliverables

.

.

.

Major Activities

Zigg mapping

What How

Zigg mapping

Zig-

zagging

What How



DPB1-2: Contract

Awarding Process




Centric Process)

FR1: Awarded Contract(s)

FR2: Ranked & Prioritized Critical Customer Needs

FR3: Major

program

assumptions

FRB1-2-1: ID Team Members FRB1-2-2: Determine CSP FRB1-2-3: Define Scope

DPB1-8-1: Give IPT

access rights

DPB1-8-2 : Online tools or a

procedure (e.g. OCS)-

Automatic /Manual

DPB1-8-3: Version

control (

automatic/manual)


FRB1-8-3: Control project data


Data Environment

(IDE)


FR4: Project PlanDPB1-2:-1 Identify skills for

project and form IPT (101)


DPB1-2-2 CSP

Procedure)


DPB1-2-3 Project

Charter


DPB1-2-4 ARDEC MS

Project Template


Develop overall,


Need to put the activities in the right swim lanes

Axiomatic Design Top Down

Synthesized Maps

Level 2

Level 1

Level 1 Map: ProcessLevel 1 Map: ProcessLevel 1 Map: ProcessLevel 1 Map: Process

Process Maps


Level 3

Level 2 Map: Procedure

Level 3 Map: Task

Process Maps

DPB1-2: Contract Awarding Process

DPB1-1 : Gather & Process VOC, identify

critical customer needs (Customer Centric

Process)

FR1: Awarded Contract(s)

FR2: Ranked & Prioritized Critical Customer Needs

FR3: Major

program

assumptions

FR4: Project PlanDPB1-2:-1 Identify skills for project and form IPT (101)


DPB1-2-2 CSP Procedure)


DPB1-2-3 Project Charter


DPB1-2-4 ARDEC MS

Project Template


DPB1-8-1: Give IPT access rights

DPB1-8-2 : Online tools or a procedure (e.g.

OCS)-Automatic /Manual

DPB1-8-3: Version control (

automatic/manual)


FRB1-8-3: Control project data

Develop overall,


Establish Integrated Data Environment (IDE)


DPTBC1: Conduct Risk Management (104)

FRTBC1:CSP RequirementsGap Analysis

DPTBC8: Involve customers & suppliers early & often

FRTBC8: CSP Validate development work done in this block/phase

DPTBC5: Conduct Critical Parameter

Management Process

FRTBC5: Updated critical parameter management database

DPTBC2: Update Project Plan; Specific Tasks &Activities for each Phase

must be defined & linked to Deliverables.Includes an integrated MS Project/EPM schedule. (101)

FRTBC2: Next Phase detailed plans & constraints

DPTBC7: Report CSP and Risk variances when breached between gates

FRTBC7: Communicate CSP & Risk Status

DPTBC4: ARDEC IP PROCESS

FRTBC4: DocumentedIntellectual Property Status

DPTBC6: Develop process for problem capture and resolution tracking linked to lessons learned database

FRTBC6: Documented Lessons Learned

DPTBC3: Develop & refine technology opportunities and associated business case

FRTBC3: Input to product portfolio financial business case document

Axiomatic Design Advantages

• Hierarchical mapping process

– Systematic design mapping generator

– Way to deal with complexity (deal with small number of steps at a time)

– Logical precedence relationships are easily discovered

• Building block approach

– Lower level maps replaces higher levels when required

• Quality Check


• Quality Check

– Missed deliverables

– Missed activities

– Ill-worded deliverables

– Ill-worded activities

– Week relationships between deliverables and activities

• Coupling treatment is readily available …uncoupled/decoupled matrices

– Within a Vector block and across blocks (repetitive procedures)

• Linked nicely to Computer-Aided DFSS (product design)

Computer-Aided DFSS (CA-DFSS)

Res

pons

e +

Sen

sitiv

ityM&S Model

Des

ign

Poi

ntNoise Factors

• Use the “most probable point” instead of random samples for hardware DV

Reliability/Robustness

Reduction of DV Test Sample

Yes

Influence

Control Factors

AD Design Matrix


• Assess reliability & robustness by incorporating noise (variability)

• Identify parameters contribution to reliability & robustness for design direction

• Identify the critical design parameter combination

• Parameter Design to find optimal control factor setting to desensitize performance without controlling variability

• Tolerance Design to select economical tolerance allocation or to control variability

CA-DFSSAssessment

MeetRequirement?

Robustness

Design Point (Nominal and or Tolerance)

CA-DFSSOptimization

InfluenceFactors

No

SSPI Has a Complete Suite of CA-DFSS Software

References

• El-Haik, B., “Axiomatic Quality & Reliability”, John Wiley & Sons, Inc.,

New York, April, 2005.


Q’s?


Overall Design Mapping…

{VOC/CTQs}...

{FRs}...

{DPs}...

{PVs}...

Relate map map

[A] [B][C]


Customer Domain

Functional Domain

Physical Domain

Process Domain

[C] = [A] * [B]

Diagonal Matrix [ ]Triangular Matrix [ ]Full Matrix [ ]

Diagonal Matrix [ ]Triangular Matrix [ ]Full Matrix [ ] *??? =

Possibilities/Probabilities of Design?

Legend

: Coupled matrix (Upper, lower & diagonal)

: Upper triangular matrix

: Lower triangular matrix

: Diagonal matrix


[A] \[B][A] \[B]

Probability of an overall uncoupled design is…Probability of an overall decoupled design is…

Probability of an overall coupled design is…

Design is a mapping process…

FRs

FR1

FRs

FR1FR1

PVs

PV1

PV11 PV12

PVs

PV1

PV11 PV12

PV1

PV11 PV12

Process Mapping

FRs

FR1FR1

PVs

PV1

PV11 PV12

PVs

PV1

PV11 PV12

PV1

PV11 PV12

FRs

FR1FR1

PVs

PV1

PV11 PV12

PVs

PV1

PV11 PV12

PV1

PV11 PV12

FRs

FR1FR1

PVs

PV11PV11

PVs

PV11PV11

Customer Mapping Physical Mapping

CAs FRs

FR1

FR11 FR12

DPs

DP1

DP11 DP12 PV11PV11

PV1

PV11 PV12


FR11FR12

FR1

FR11FR12

FR1

FR11FR12PV11 PV12PV11 PV12PV11 PV12

FR1

FR11FR12

FR1


FR1

FR11FR12

FR1


FR1

FR11FR12

FR1

FR11FR12PV11PV11PV11PV11FR11 FR12 DP11 DP12 PV11PV11PV11 PV12

Design is a continuous mapping activity between 4 domains:

CAs��FRs��DPs��PVs

Customer Attributes Domain

Functional Requirements

Domain

Design Parameters Domain

Process Variables Domain

Example

FRsFRs PVsPVsFRs PVsPVsFRs PVsPVsFRs PVsPVsCAs FRs DPs

Frig Manfg. Frig

Preserve Stop bacteria


Other DPs (concepts) to do FR=“Stop Bacteria” Cold, heat, radiation, salt …

Customer Attributes Domain

Functional Requirements

DomainDesign Parameters Domain

Process Variables Domain

Frig Manfg.

ProcessesFrig

Preserve

beefStop bacteria

Documents

VECTOR Detail Design: The Application of Axiomatic Design