3274090

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D e s i g n

f o r

DFSS-1Copyright 2003 Cummins, Inc. All Rights Reserve.

Copyright 2000-2002 Sigm! "re!#through $echnologies, Inc. %se &ith permission.

Executing Robust Design

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Why We Need to Reduce Variation

C o s t

Low Variation;

Minimum Cost

LSL

LSL

USL

USL

Nom

Nom

C o s t

High Variation;High Cost

LSL

LSL USL

USLNom

Nom

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DFSS-'Copyright 2003 Cummins, Inc. All Rights Reserve.


Purpose of this Module

To introduce a variation improvement investigationstrategy – Can noise factors be manipulated?

To provide the !"!TA# steps to design$ e%ecute$

and analy&e a variability response e%periment To provide the !"!TA# steps to optimi&e a design

for both mean and variation effects

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DFSS-(Copyright 2003 Cummins, Inc. All Rights Reserve.


Objecties of this Module

At the end of this module$ participants will be able to :

!dentify possible variation effects from residual plots

Create a variability response from replicates

!dentify possible mean and variance ad'ustmentfactors from noise-factor interaction plots

(se the !"!TA# Response )ptimi&er to achieve a

process on target with minimum variation

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D e s i g n

f o r

DFSS-)Copyright 2003 Cummins, Inc. All Rights Reserve.


!trategies to Detect VariationE"ects

*assive Approach – "oise factors are *+$ included$ manipulated or controlled in

the e%perimental design

– *ossible variation effects are identified through analysis of

the variability of replicates from an e%perimental design

Active Approach – "oise factors AR included in the e%perimental design in

order to force variability to occur

– Analysis is similar to the passive approach

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DFSS-/Copyright 2003 Cummins, Inc. All Rights Reserve.


$ Passie Exa(ple

A and # are control factors. 4ithin each treatment combination$noise factors are allowed to naturally fluctuate. 4ithin treatmentvariation is largely driven by this bac5ground noise.

A

"

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Exa(ple output fro( a PassieDesign

The graphs at rightillustrate the type of outputwhich might be obtainedfrom a Robust *arameteresign 1%periment. #othare ain 1ffects plots with

the top row showing themain effects of factors Aand # on the mean andthe bottom row showingthe main effects of factors

A and # on the variation.

"ote that in this e%amplethe mean and variationcan be ad'ustedindependently of eachother6

e an<

# A

> ar i a t i on<

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Exa(ple) $ Passie NoiseExperi(ent

A design engineer has evaluated the output performance of acircuit design and performed an initial capability analysis of this

design to determine if there is a problem with the mean and2or

the variability.

+tat Duality Tools Capability Analysis "ormal

< E <F!nitialG 0ower +pec E 9HG (pper +pec E 7;

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Design *apability $nalysis

!s there a problem?

61.560.058.557.055.554.052.5

LSL USL

Process Data

Sample N 100

StDev(Withi! 1.47217

StDev("verall! 1.5414

LSL 58 #ar$et %

USL 62

Sample &ea 56.25'

Potetial (Withi! apa)ilit*

"verall apa)ilit*

Pp 0.4'

PPL +0.'8

PPU 1.24

Pp, +0.'8

pm

p

%

0.45

PL +0.40

PU 1.'0

p, +0.40

")serve- Perormace

PP& / LSL 860000.00

PP& USL 0.00

PP& #otal 860000.00

p. Withi Perormace

PP& / LSL 882'24.02

PP& USL 47.'5

PP& #otal 882'71.'7

p. "verall Perormace

PP& / LSL 871474.48

PP& USL 36.''

PP& #otal 871570.81

Withi

"verall

Process *apability of +,-nitial

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D e s i g n

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DFSS-1'Copyright 2003 Cummins, Inc. All Rights Reserve.


./ 0ull 0actorial Experi(ent

A ;

8

full factorial has been designed to determine if four factorshave an effect on the mean and2or variability of voltage drop<FB. There are five replicates for a total of H= runs$ with nocenter points or bloc5s. – Resistor R AB

– !nductor 0 #B

– Capacitor C; 1B – Capacitor C;I 3B

4or5sheet: Passive Design/

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DFSS-1(Copyright 2003 Cummins, Inc. All Rights Reserve.


Passie $nalysis Road(ap 1 Part ,2for Mean Only3

Analy&e the response of interest – 3actorial *lots ain 1ffects$ !nteractionB

– +tatistical Results A")>A table and p-valuesB

– Residual *lots by factor

Reduce model using statistical results

(se the residuals plot to evaluate potential e%istence

of variation effects – !f residuals plot indicates a possible variation effect$ go to

*assive Analysis Roadmap - *art ;

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DFSS-1)Copyright 2003 Cummins, Inc. All Rights Reserve.


-nteraction Plot

#ased on the interaction plot$ a few of the interactions may besignificant. Chec5 the statistical output for verification.

+tat )1 3actorial 3actorial *lots !nteraction *lot

$

E

0

4

51 1'.512.5 636'

60.0

57.5

55.0

60.0

57.5

55.0

60.0

57.5

55.0

10

20

1

5

12.5

1'.5

-nteraction Plot 2data (eans3 for +,

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Main E"ects Plot

The main effects plot indicates that factors # and 1 have thelargest effects. 3actor A also has a moderate positive effect.

3actor 3 does not seem to be important. 0ets loo5 at the results.

+tat )1 3actorial 3actorial *lots ain 1ffects *lot

M e a n o f + ,

2010

58

57

56

55

5451

1'.512.5

58

57

56

55

54636'

Main Effects Plot 2data (eans3 for +,

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0actorial $nalysis

A preliminary loo5 at the statistical output of the e%perimentindicates factor 3 may not be significant. id we ma5e amista5e by including it in the e%perimental design?

J "ote that the -way and 8-way interactions are still in the model but notpresented in the output above

+tat )1 3actorial Analy&e 3actorial esign

Estimated Effects and Coefficients for Y1 (coded units)

Term Effect Coef SE Coef T P

Constant 55.991 0.2041 274.27 0.000A 2.! 1.1"1 0.2041 5.79 0.000

# $.192 $1.59! 0.2041 $7."2 0.000

E .12 1.!5! 0.2041 ".11 0.000

% 0.4! 0.21 0.2041 1.1 0.2!2

A&# 0.17" 0.0"9 0.2041 0.4 0.!!5

A&E 0.002 0.001 0.2041 0.01 0.995

A&% $0.1" $0.0!9 0.2041 $0.4 0.77

#&E $0.9 $0.4!! 0.2041 $2.2" 0.02!#&% $0.!!2 $0.1 0.2041 $1.!2 0.110

E&% $0.007 $0.004 0.2041 $0.02 0.9"5

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DFSS-1/Copyright 2003 Cummins, Inc. All Rights Reserve.


Reduce Model to !ignicant#er(s

)ur final model indicates that factors A$ #$ and 1 aresignificant$ along with interactions #1$ #3$ A#3$ and

#13$ using a p-value cut-off of =.;



Constant 55.991 0.194! 2"7.74 0.000

A 2.! 1.1"1 0.194! !.07 0.000

# $.192 $1.59! 0.194! $".20 0.000

E .12 1.!5! 0.194! ".51 0.000

% 0.4! 0.21 0.194! 1.19 0.29

#&E $0.92 $0.4!! 0.194! $2.40 0.019

#&% $0.!!2 $0.1 0.194! $1.70 0.09A&#&% $0.51 $0.25! 0.194! $1.2 0.192

#&E&% 0."" 0.419 0.194! 2.15 0.05

S ' 1.7404! $S ' 7.11* $S(ad+) ' 70.0"*


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#he Role of Residual Plots in RD

!n Robust *arameter esign$ the residual plots can show thepossibility for a variation effect

Remember from A")>A and Regression$ we stated one of the

assumptions on the residuals was constant variance and we

chec5ed this via plots


Choose Kraphs Residuals vs >ariables A # 1 3

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What Next'

After reducing the model$ the Residuals versus 3actor 3/ plotstill indicates that 3 contributes to a variation effect. This finding

should encourage us to move further in the analysis of this data

to create a variability response and analy&e the data. Thus we

move on to *art ; of the roadmap.

0

! t a n d a r d i 5 e d R e s i d u a l

6368676665646'

'

2

1

0

+1

+2

+'

Residuals Versus 0(respose is 1!

+tat )1 3actorial

Analy&e 3actorial esign

Choose Kraphs

Residuals vs >ariables 3

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Create a >ariability Response Analy&e >ariability

– 3actorial *lots ain 1ffects$ !nteractionB


– Reduce model using statistical results

Compare main effects plots for mean and variabilityto determine which are ean Ad'ustment 3actors andwhich are >ariance Ad'ustment 3actors or bothB

(se the ultiple Response )ptimi&er to find optimal

settings of the factors – ean on target

– inimum variability

*erform a capability study 2 analysis on the resultingfactor settings

Passie $nalysis Road(ap 1 Part .2if Variation e"ect present3

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*reate a Variability Response

4e are now going to use the replications to ma5e anew response in order to model the variability. )ncewe have modeled the variability$ we can use the!"!TA# Response )ptimi&er to find the settings ofthe control factors that will put < on target with

minimum variation.

!"!TA# ma5es this easy with a pre-processing ofthe responses in preparation for a variability analysis

<ou will see that !"!TA# will use the standarddeviation as the measure of variability$ rather than thevariance – the results are e,uivalent

6 N t l 7 2!t d d D

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6ses Natural 7og 2!tandard Deof +3

All of the statistical techni,ues that we are using to analy&e this)1 assume that the data is symmetric because we aretesting for mean differencesB

(nfortunately$ when we use a calculated standard deviation as aresponse$ we do not meet this assumption because thesampling distribution of variances is e%pected to be s5ewed$

hence the distribution of standard deviations would also bes5ewed

Raw +t ev 0n +t evB

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*reate a Variability Response

+tat )1 3actorial *re-*rocess Responses for Analy&e >ariability

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$naly5e the Variability

Analysis of the variability will be essentially identical to theanalysis for the mean

4ill select the Terms/ to estimate in the model

4ill use the *areto of 1ffects Kraph/ in order to facilitate the

first model reduction

+tat )1 3actorial

Analy&e >ariability

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$naly5e the Variability

$RS RAS

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Pareto *hart of the E"ects

#ecause we dont have any degrees of freedom for error$ wemust loo5 at the *areto of effects to decide which term to drop

into the error and begin to reduce the model

# e r (

Effect

D

D

D

D

D

D

D

D

1.41.21.00.80.60.40.20.0

0.1'0actor

Name

D

Pareto *hart of the Effects(espose is at9ral lo$ o StDev1: lpha ; 0.20!

Leth<s PS ; 0.0878'1'

rop A#

interaction first

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-nteraction Plot for !tDe+,

The interaction plot indicates a moderately strong interaction betweenfactors A L 1 and A L 3


$

E

0

4

51 1'.512.5 636'

'

2

1

'

2

1

'

2

1

10

20

1

5

12.51'.5

-nteraction Plot 2data (eans3 for !tDe+,

4here shoul

5!ctors A, ", !n F 6e set in

orer to

minimi7e the

v!ri!6ility in

volt!ge rop,

819

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Main E"ects Plot for !tDe+,

3actor 3 has the largest effect on the variability. !ncreasing 3 should

reduce variability. #ut what did the interaction plot show? 3actor A is the ne%t strongest. +et A E F=. 4hat did the interaction plot

show? 3actors # and 1 are wea5 but what did the interaction plot show?

M e a n

o f ! t D e + ,

2010

2.5

2.0

1.5

1.0

0.5

51

1'.512.5

2.5

2.0

1.5

1.0

0.5

636'

Main Effects Plot 2data (eans3 for !tDe+,


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Deter(ine Mean 8 Variation E"ects

The graphs at right allowus to directly compareeach factors singulareffect on both the meanand variation

#ased on these graphs$ – 3actors # and 1 are

ean Ad'ustment3actors since theyaffect the mean withlittle or no effect on thevariability

– 3actor 3 is a >ariance Ad'ustment 3actor

since it affects thevariability with little orno effect on the mean

– 3actor A appears toaffect both mean andvariability

M e a n o f + ,

2010

58

57

56

55

54

51

M e a n o f + ,

1'.512.5

58

57

56

55

54

636'

M e a n o f !

t D e + ,

2010

2.5

2.0

1.5

1.0

0.5

51

M e a n o f !

t D e + ,

1'.512.5

2.5

2.0

1.5

1.0

0.5

636'

Main Effects Plot 2data (eans3 for +, Main Effects Plot 2data (eans3 for +,

Main Effects Plot 2data (eans3 for !tDe+, Main Effects Plot 2data (eans3 for !tDe+,

A55 ects "oth A55ects e!n A55ects e!n A55ects :!ri!tion

9uality *hec:) !tatus of +our

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9uality *hec:) !tatus of +ourModels

(se the +how esign/ iconto chec5 on the status of the

analysis. <ou should ma5e

sure that the correct model

has been fit for each

response that you intend to

specify in the response

optimi&er.

As shown in this window$

models have been fit for both

the <F and +tev<F

responses

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Multiple Response Opti(i5er

+tat )1 3actorial Response )ptimi&er

+et the 4eight for <F to F= to ensure hitting 7=$ tight lower L upper range

Read first-guess/ target L upper values for +tev<F from interaction plots – "ote that +tev<F is in regular units here$ ")T logged units6

3or +tev<F$ set weight low to protect against a bad first guess

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DFSS-3)Copyright 2003 Cummins, Inc. All Rights Reserve.


Multiple Response Opti(i5er

4e use the multiple response optimi&er to provide a stac5edmain effects plot. This plot allows us to interactively manipulate

the values of each factor in the model and see the effect on both

the mean and the variation.

<ou can use the red sliders to tune each of the factors

Mi

0o=.I7IH

)ptimal

Cur

d E =.HNHI7

inimum+tev<F

d E =.IIHH8

Targ: 7=.=

y E =.9N;9

y E 7=.===F

7.=

7I.=

F;.9=

F.9=

F.=

9.=

F=.=

;=.=# 1 3 A

OF.8HNHP OF.=P OF.9=P O7I.=P

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6se the E;uations to *onr( +,

0ets use the model coefficients to predict and seethat it matches ma5e sure to use un-codedB6

3rom the optimi&ed solution$ A E F.8HNH$ # E F$ 1 E

F.9$ 3 E 7I

Y1 = $22.0994 0.214!70& A 45.2!19&B 4.71125&E 0.24270"&F $ .2!279&B&E $ 0.!07!7!&B&F 0.00010"9""& A &B&F 0.04271"&B&E&F

Y1 = $22.0994 0.214!70&13.4878 45.2!19&1

4.71125&13.5 0.24270"&69 $ .2!279&1&13.5 $0.!07!7!&1&69 0.00010"9""&13.4878&1&69 0.04271"&1&13.5&69

Y1 = 60.00013 as seen in te otimi6er indo

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6se the E;uations to *onr( !tDe+,

Again$ ma5e sure to use the un-coded coefficients6

Again$ A E F.8HNH$ # E F$ 1 E F.9$ 3 E 7I

lnStDevY1 = 15.4015 $ 0.00177"& A 0.727714&B $0.927015&E $ 0.05!!905&F $ 0.152!2!& A &B 0.05!52& A &E $ 0.0097"99"& A &F 0.024219"&B&F

0.009"241& A &B&E $ 0.002"29!!&B&E&F 0.000017& A &B&E&F

lnStDevY1 = 15.4015 $ 0.00177"&13.4878 0.727714&1 $ 0.927015&13.5 $ 0.05!!905&69 $0.152!2!&13.4878&1 0.05!52&13.4878&13.5 $

0.0097"99"&13.4878&69 0.024219"&1&69 0.009"241&13.4878&1&13.5 $ 0.002"29!!&1&13.5&69 0.000017&13.4878&1&13.5&69

lnStDevY1 = $0.5577

StDevY1 = e-0.5577 = 0.57253 as seen in te otimi6er

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0inal Design *apability $nalysis

id we achieve our ob'ectives?

61.6061.0560.5053.3553.4058.8558.'0

LSL USL

Process Data

Sample N 100StDev(Withi! 0.120084


LSL 58

#ar$et %

USL 62

Sample &ea 60.'18'


"verall apa)ilit*

Pp 5.75

PPL 6.66

PPU 4.8'

Pp, 4.8'

pm

p

%

5.55

PL 6.44PU 4.67

p, 4.67

")serve- Perormace

PP& / LSL 0.00

PP& USL 0.00

PP& #otal 0.00

p. Withi Perormace

PP& / LSL 0.00

PP& USL 0.00

PP& #otal 0.00


PP& / LSL 0.00

PP& USL 0.00

PP& #otal 0.00

Withi

"verall

Process *apability of +,0inal

wor5sheet passive capability /

+tat Duality Tools Capability

Analysis "ormal

< E <F3inalG 0ower +pec E 9HG(pper +pec E 7;

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DFSS-'0Copyright 2003 Cummins, Inc. All Rights Reserve.


Re(e(ber the #&o !trategies'

4e 'ust reviewed the *assive Approach – "oise factors are *+$ included$ manipulated or controlled in

the e%perimental design

– 4e analy&ed the variability of replicates from an

e%perimental design

"ow we will loo5 at the Active Approach – "oise factors AR included in the e%perimental design in

order to force variability to occur

–4e will see that the analysis is similar to the passiveapproach

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#he $ctie $pproach

A factorial e%periment is performed using Control A" "oisefactors in the same e%periment. Analysis can be performed by

characteri&ing ControlJ"oise interactions only or by moving

forward to analy&e the variability by dropping the noise factors

into the error term.

*ros – +imple e%tension of standard e%perimental techni,ues

– Kuarantees noise in the "oise factors

– *rovides for fle%ibility in analysis methods

– Can allow for reduced replication

Cons – Re,uires ability to manipulate and control "oise factors

– )ptimal designs for minimi&ation of unneeded effects noise by

noise interactionsB can be difficult to create

Exa(ple) $n $ctie Noise

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control factors

F noise factor

;8 full factorial design

Two Approaches to Analysis – (se only interpretation of interaction plots to choose settings

of the control factors to minimi&e effect of noise

– odel the variability by dropping the noise factors into the

error and analy&e li5e the passive approach

Exa(ple) $n $ctie NoiseExperi(ent

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$ctie $nalysis Road(ap < Plots Only

Create and e%ecute with noise included as a factor Analy&e the response of interest

– 3actorial *lots ain 1ffects$ !nteractionB


– Reduce model using statistical results

Review !nteractions *lot – !nterpret the interaction plots to loo5 for evidence of variation effects

Review ain 1ffects *lot if applicableB

(se the ultiple Response )ptimi&er to find the optimal settings

of the factors such that the mean is on target

– 4ill force in settings obtained from the interaction plots *erform a capability study 2 analysis on the resulting factor

settings

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DFSS-''Copyright 2003 Cummins, Inc. All Rights Reserve.


Exa(ple) $n $ctie Noise Experi(ent

An engineer is interested in improving the stability androbustness of a filtration product

Review the capability of the current performance to determine

the opportunity to apply robust design techni,ues

+tat Duality Tools Capability Analysis "ormal

< E <8!nitialG 0ower +pec E 7=G (pper +pec E H=

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DFSS-'(Copyright 2003 Cummins, Inc. All Rights Reserve.


Design *apability $nalysis

4hat conclusions can you draw from this graph?

807672686460

LSL USL

Process Data

Sample N 100

StDev(Withi! 4.006'8

StDev("verall! '.37663

LSL 60

#ar$et %

USL 80

Sample &ea 70.'21


"verall apa)ilit*

Pp 0.84

PPL 0.87

PPU 0.81

Pp, 0.81pm

p

%

0.8'

PL 0.86

PU 0.81

p, 0.81

")serve- Perormace

PP& / LSL 0.00

PP& USL 10000.00

PP& #otal 10000.00

p. Withi Perormace

PP& / LSL 4335.46

PP& USL 7848.20

PP& #otal 1284'.66


PP& / LSL 4724.40

PP& USL 7467.87

PP& #otal 12132.28

Withi

"verall

Process *apability of +/-nitial

Exa(ple) $n $ctie Noise

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DFSS-')Copyright 2003 Cummins, Inc. All Rights Reserve.


Exa(ple) $n $ctie NoiseExperi(ent

The device contains several control factors fromwhich three were identified as )1 candidates – *ressure AB

– Concentration #B

– +tir Rate CB

Ambient Temperature was identified as being

significant$ but not economically controllable – Temperature would not change appreciably during the time

in which it would ta5e to e%ecute a three factor e%periment – ecided to include it as a factor in the design to force it to

change

– Call this 3actor K

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#he Experi(ental Design A ;8-F fractional design Res !>B was re'ected because

the ;-way interactions are of great interest in thise%periment

A ;8 full factorial design was used

#ecause of time constraints$ only F replicate was

performed The variables are listed below:

– A E *ressure

– # E Concentration

–

C E +tir Rate – K E Temperature

The data is in wor5sheet Active Design/

)pen wor5sheet Active Design/ within Robust

Design.mpj /

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0actorial $nalysis

This )1 is an unreplicated$ 8-factor full factorial – 4e need to create the *areto of 1ffects/ chart


# e r (

Effect

D

DD

D

D

DD

D

20151050

0.08actor

=

Name

D

Pareto *hart of the Effects(respose is 4: lpha ; .20!

Leth<s PS ; 0.05625

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DFSS-'/Copyright 2003 Cummins, Inc. All Rights Reserve.


0it the Reduced Model


#ased on the p-values$ the AJK and #JK and CJK interactionsare important. +ince we have identified some importantcontrolJnoise interactions$ the ne%t step is to e%amine theinteraction plots.



Constant 70.0"1 0.00!250 1121.00 0.000

A 5.9"7 2.994 0.00!250 479.00 0.000

# 9.7"7 4."94 0.00!250 7".00 0.000

C 14.!12 7.0! 0.00!250 11!9.00 0.000

8 21."7 10.!94 0.00!250 1711.00 0.000

A&# $0.0" $0.019 0.00!250 $.00 0.05"

A&8 $0.0"7 $0.044 0.00!250 $7.00 0.00!

#&C $0.0!2 $0.01 0.00!250 $5.00 0.015#&8 $1".0" $9.019 0.00!250 $144.00 0.000

C&8 1!.!" ".19 0.00!250 11.00 0.000

A&#&C 0.0!2 0.01 0.00!250 5.00 0.015

A&#&8 0.17 0.0!9 0.00!250 11.00 0.002

A&#&C&8 0.07 0.019 0.00!250 .00 0.05"

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f o r

DFSS-(0Copyright 2003 Cummins, Inc. All Rights Reserve.


-nteraction Plot

The interaction plot show the valuable interactions available tothe designer. 0ets ta5e a closer loo5 at the strongest ones.


$

*

=

4

51 200150 1+1

100

75

50

100

75

50

100

75

50

10

20

1

5

150

200

-nteraction Plot 2data (eans3 for +/

n

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f o r



-nteraction Plot < $ *loser 7oo:

The two interaction plots at right

indicate that both # and C can be

e%ploited to desensiti&e <8 to the

noise variable K

– !f # is set at its high level$ the

slope of the K effect line is

minimi&ed – !f C is set at its low level$ the

slope of the K effect line is also

minimi&ed

To minimi&e output variation due to

noise in ambient temperature KB$

the above two settings should becontrolled in the design

=

M e a n

1+1

100

80

60

40

1

5

=

M e a n

1+1

100

80

60

40

150

200

-nteraction Plot 2data (eans3 for +/

n

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Main E"ects Plot

+ince factor A is not involved in a significant interaction and itsmain effect is significant$ we should ta5e a loo5 at its main effectplot to see if there is some potential value in controlling A

This plot indicates that factor A has about Q2- units of controlover the nominal value of <8. Thus$ if manipulating one of theother factors ta5es the mean value off target$ this factor could beused to e%ert some control over the mean value of <.


$

M e a n o f + /

2010

7'

72

71

70

63

68

67

Main Effects Plot 2data (eans3 for +/

n

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D e s i g n

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Ne& !ettings ) *apability $nalysis

# was set to 9$ C was set to F9=$ A was left at nominal F9B !t appears that the changes to # L C were successful in reducing

variation in <8 but the mean is now off target

(se factor A to ad'ust bac5 to target6

78757263666'60

LSL USL

Process Data

Sample N 100

StDev(Withi! 2.06587


LSL 60

#ar$et %

USL 80

Sample &ea 67.838


"verall apa)ilit*

Pp 1.55

PPL 1.22

PPU 1.88

Pp, 1.22

pm

p

%

1.61

PL 1.27

PU 1.35

p, 1.27

")serve- Perormace

PP& / LSL 0.00

PP& USL 0.00

PP& #otal 0.00

p. Withi Perormace

PP& / LSL 65.30

PP& USL 0.00

PP& #otal 65.30


PP& / LSL 113.37

PP& USL 0.01

PP& #otal 113.38

Withi

"verall

Process *apability of +/Valid

n %o& (uch should &e shift

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f o r

DFSS-('Copyright 2003 Cummins, Inc. All Rights Reserve.


%o& (uch should &e shiftfactor $'

+et up the responseoptimi&er to target N=. Thelower and upper limits arenot important since we willmanually manipulate this.

+et factor #E9 and factorCEF9=. The optimi&er

indicates a nominal<8E7N.N$ very close to thatobserved in the validationstudy.

3inally$ slowly slide the barfor factor A to the right

while observing thepredicted value of <8.This indicates that anominal setting of AEFH.Hshould achieve <8EN=.

Mi

0o=.III8

"ew

Cur

d E =.III8

Targ: N=.=<8

y E 7I.IIHN

-F.=

F.=

F9=.=

;==.=

F.=

9.=

F=.=

;=.=# C K A

OFH.H=P O9.=P OF9=.=P O-=.==N7P

4or5sheet active design”

+tat )1 3actorial Response )ptimi&er

Mi

0o=.=====

"ew

Cur

d E =.=====

Targ: N=.=

y E 7N.N9=7

-F.=

F.=

F9=.=

;==.=

F.=

9.=

F=.=

;=.=

# C K A

OF9.=P O9.=P OF9=.=P O-=.==N7P

n Ne& !etting for $ ) *apability

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f o r

DFSS-((Copyright 2003 Cummins, Inc. All Rights Reserve.


Ne& !etting for $ ) *apability$nalysis

4hen we shift factor A to this new nominal value$ we succeed atshifting the response to put it on target without degrading the

variation

78757263666'60

LSL USL

Process Data

Sample N 100

StDev(Withi! 2.0310'

StDev("verall! 2.2058'

LSL 60

#ar$et %

USL 80

Sample &ea 70.2302


"verall apa)ilit*

Pp 1.51

PPL 1.56

PPU 1.47

Pp, 1.47

pm

p

%

1.53

PL 1.64

PU 1.55

p, 1.55

")serve- Perormace

PP& / LSL 0.00

PP& USL 0.00

PP& #otal 0.00

p. Withi Perormace

PP& / LSL 0.4'

PP& USL 1.71

PP& #otal 2.14


PP& / LSL 1.54

PP& USL 5.'7

PP& #otal 6.31

Withi

"verall

Process *apability of +/Reduced

n

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D e s i g n

f o r

DFSS-()Copyright 2003 Cummins, Inc. All Rights Reserve.


!u((ary

>ariation improvement strategies can ta5e two forms: – *assive Approach

– Active Approach

The choice of which strategy to use depends on the ability to

control or manipulate noise factors at least for the duration of

the e%perimentB +tandard full and fractional designs can be used

>ariation effects must be calculated using replications

A log transform of the variability response is automatically used

to minimi&e the effects of asymmetry in the variance distribution

The response optimi&er can be used to simultaneously optimi&eboth mean and variability responses

A validation study must be made at the end of a Robust

*arameter esign study

n

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D e s i g n

f o r Objecties Reisited

At the end of this module$ participants should be able to :

!dentify possible variation effects from residual plots

Create a variability response from replicates

!dentify possible mean and variance ad'ustmentfactors from noise-factor interaction plots

(se the !"!TA# Response )ptimi&er to achieve a

process on target with minimum variation

Complete validation capability studies

3274090

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