9-07 factorial planning process

8/2/2019 9-07 Factorial Planning Process

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Webinar Se tember 19, 2007

ac or a es gnPlannin Process

ar ra er a com

Stat-Ease, Inc. Stat-Ease, Inc.

[email protected] [email protected]

DOE Process 1


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Factorial Design Planning Process

ur a as ree par s:

. roa rus escr p on o eplanning process

2. Illustrate key points via an example

3. Summary

DOE Process 2


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Desi n of Ex eriments

Controllable Factors x

DOE (Design of Experiments) is:

,

in which purposeful changes

are made to input factors,

Process Responses y

causes for significant changes

in the output responses.

Noise Factors z

DOE Process 3


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Iterative Ex erimentation

DesignAnalysis

Experiment

DOE Process 4.


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Factorial Design Planning Process (1 of 2)

1. Identif o ortunit and define ob ective.

2. State objective in terms of measurable responses.

a. e ne e c ange y a s mpor an o e ec

for each response.

.

response.

.

power.

. .

the factor levels chosen determine the size ofy.)

DOE Process 5


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4. Select a desi n and:

Evaluate aliases (fractional factorials and/or

-

interaction (2FI) model.

of interest); generally use main effects (ME)

model for robust desi n use onl 1 ME .

Examine the design layout to ensure all the factor

result in meaningful information (no disasters).

DOE Process 6


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Factorial Design Planning Process IdentifyO ortunit

Tools: Brainstorming (fishbone)

Define

Outputs Voting Form State Objective utputs, y, , ontr ut on

Factors Voting Form

Measurable Responses

DOE inputs, levels, operating range Other inputs

e ec npu

Factors

e ec an appropr a e ac or a es gn

Evaluate aliases (fractional factorials

and/or blocked designs)

Select

Design

va ua e power

Examine the design layoutEvaluate

Aliases & Power

DOE Process 7ExamineLayout


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ur a as ree par s:

. roa rus escr p on o e

planning process


3. Summary

DOE Process 8


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Stent Delivery System

A stent is a wire mesh tube used to ro o en an arter

that's recently been cleared using angioplasty. The stent

is collapsed to a small diameter over a balloon catheter.s en move n o e area o e oc age.

, ,

place and forms a scaffold. This holds the artery open.

The stent sta s in the arter ermanentl holdin it o en

to improve blood flow to the heart muscle.

DOE Process 9


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1. Identify opportunity and define objective.

Relate stent deliverability and safety to process factors.

Guidelines for Brainstormin a Desi ned Ex eriment

Team Make Up: Experts

Semi-Experts or Peripheral Experts

Technicians or OperatorsCustomers

Scheduling: Two meetings no more than 2 days apart.

First day spend approximately 1 to 2 hours, , .

Second day spend approximately 2 to 4 hours

developing DOE.

DOE Process 10


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2. State ob ective in terms of measurable res onses.

Deliverability is quantified by Trackability and Pushability;

safety is quantified by Burst pressure. Want to estimate, .

a. Define the change (y) that is important to detect for.

b. Estimate experimental error () for each response.

c. Use the si nal to noise ratio / to estimatepower.

DOE Process 11


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Outputs Voting Form

Evaluation of Out uts Votin Form

Response Type of Response Team Member's Ranking of Importance

Output (y) (V) Variable of the Responses

(D) Destructive 1: low rank; 5: high rank

Average Standard Deviation

(A) Attribute

M1 M2 M3 M4 M5 M6 M7 M8

DOE Process 12


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.

Response Unit of Specification Practical Std %MC*

Y1: Burst psig Maximize 6 8 27%

Y2: Push g/cm Maximize 15 30 75%

* % measurement contribution

Y3: Track g*cm Minimize 10 6 19%

DOE Process 13


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3. Select the in ut factors to stud . Remember that the

factor levels chosen determine the size ofy.)

Typical factors include:

Lengths and diameters of various components, e.g.

tip, balloon, catheter, etc.

Materials used for the components.

, . . ,

balloon is folded, etc.

, ,

the balloon, etc.

DOE Process 14


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Factors Voting Form

Evaluation of Factors Voting Form

Factor Name Type of Factor Team Member's Ranking of Importance

Input (x) (C) Control of the Factors

(N) Noise 1: low rank; 5: high rank

Average Standard DeviationM1 M2 M3 M4 M5 M6 M7 M8

DOE Process 15


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Factors

Unit of F M V B Target Range Comments

Factor Measure

F: Fixedfactors that do not change for the duration of the experiment, e.g. One batch of raw

material, one operator, etc.

: on or ac ors a owe o vary ur ng e course o e exper men an w emonitored, e.g. temperature, humidity, etc.

V: Vary factors allowed to vary, but will not be monitored, e.g. temperature, humidity, etc.

B: Block factors used to block ex erimental runs, e. . time of da , machine, etc.

DOE Process 16


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3. Select the input factors to study.

Factor Type Low Level () High Level (+) Operating Range

A numeric

1 +1B numeric 1 +1

C numeric 1 +1

D numeric 1 +1

E numeric

1 +1

F numeric 1 +1There were 11 factors: 10 numeric and 1 categoric;

the actual factor details are proprietary.

G numeric 1 +1

H numeric 1 +1

J numeric 1 +1

K numeric 1 +1

L categoric L1 L2

DOE Process 17


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4. Select a desi n want resolution V:


Evaluate power (desire power > 80% for effects

Evaluation; Order: Main effects

xam ne e es gn ayou o ensure a e ac or

combinations are safe to run and are likely to

DOE Process 18


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Candidate resolution V desi ns:

A regular fraction requires a 211-4 or 128 runs.

n rregu ar a ge ra c rac on requ res runs.

A MR5* fraction requires 68 runs.

Add center points to check for curvature.

level of the categoric factor for a total of 76 runs.

* Small, Efficient, Equireplicated Resolution V Fractions of 2k designs and their Application to

Central Composite Designs, Gary Oehlert and Pat Whitcomb, 46th Annual Fall Technical

Conference, Friday, October 18, 2002.

DOE Process 19

. . .


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1. Build an 11 factorMR5 desi n the first ten factors are

numeric and the last factor is categoric). Use the default

factor names (letters A L) and levels (1 for numeric

.

2. Add 4 center points. (Because factor L is categoric the.

3. There are three responses:

DOE Process 20


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MR5 Design

-

(2FIs) are partially aliased with scores three-factor (and

hi her interactions. But MEs and 2FIs are not aliasedwith one another.

e ree ac or an g er n erac ons are gnore

during design evaluation:

No aliases found for 2FI Model

DOE Process 21


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MR5 Design

Power is reported at a 5.0% alpha level to detect the specified signal/noise ratio.

ecommen e power s a eas .

Burst psig

Si nal (delta) = 6.00 Noise (si ma) = 8.00 Si nal/Noise (delta/si ma) = 0.75A B C D E F G H J K L

85.6% 85.6% 85.7% 85.6% 85.5% 85.3% 85.9% 86.0% 85.9% 85.8% 88.9%

Signal (delta) = 15.00Noise (sigma) = 30.00 Signal/Noise (delta/sigma) = 0.50A B C D E F G H J K L

. . . . . . . . . . .

Track g*cm

Signal (delta) = 10.00Noise (sigma) = 6.00 Signal/Noise (delta/sigma) = 1.67

99.9% 99.9% 99.9% 99.9% 99.9% 99.9% 99.9% 99.9% 99.9% 99.9% 99.9%

DOE Process 22


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MR5 Design

~

1. Increase design size: replicating the design

= ~ .No there are too many runs to be practical.

= . us .

a difference of 15 g/cm.

=us

variance, we determine that the push measurement

contributes most (75%) of the variation.es repea ng e pus es no rep ca ng e

DOE runs) to reduce is the answer.

DOE Process 23ee nex s e.


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MR5 Design

2 2 230 & = = +

900 225 675 %Contribution 675 900 75%= + = =

a e ree n epen en pus measuremen s or eac run.

Enter the average of the measurements as the response:

2 MeasurementAverageThen by the CLT = :n

2

Push

675225 450 %Contribution 50%

3

= + = =

Push

15450 21 0.71

21

= = =

DOE Process 24


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MR5 Design

Power at 5 % al ha level for effect of

Term StdErr** VIF Ri-Squared 0.71 Std Dev 0.75 Std Dev 1.67 Std Dev

A 0.12 1.02 0.0148 81.6 % 85.6 % 99.9 %

B 0.12 1.01 0.0140 81.7 % 85.6 % 99.9 %

C 0.12 1.01 0.0109 81.8 % 85.7 % 99.9 %

D 0.12 1.01 0.0139 81.7 % 85.6 % 99.9 %

. . . . .

F 0.12 1.02 0.0237 81.3 % 85.3 % 99.9 %G 0.12 1.01 0.0070 81.9 % 85.9 % 99.9 %

. . . . . .

J 0.12 1.01 0.0070 81.9 % 85.9 % 99.9 %

K 0.12 1.01 0.0101 81.8 % 85.8 % 99.9 %. . . . . .

**Basis Std. Dev. = 1.0

DOE Process 25


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Evaluate Power

Replicating runs will reduce the system error;

.

Repeating the measurement reduces only the

.

The magnitude of each of these errors and the

measurements dictates which will give the most

DOE Process 26

MR5 D i


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MR5 Design

combinations are safe to run and are likely to result

combining different components and using a variety ofassembly techniques. A knowledgeable engineer must

look at each DOE run to ascertain that the unit can be

made and will result in an operable stent deliverysys em.

DOE Process 27

St t D li S t


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Design-Expert SoftwareBurst Half-Normal Plot

Error from replicates

Shapiro-Wilk testW-value = 0.987p-value = 0.771

A: A i

99.0

99.9

A

C: CD: DE: EF: FG: GH: HJ: J l

%P

robabil

90.0

95.0 BBC

K: KL: L

Positive EffectsNegative Effects

Half-No

rm

50.0

70.0

80.0

0.0

10.0

20.0

30.0

|Standardized Effect|

0.00 4.45 8.90 13.34 17.79

DOE Process 28

St t D li S t


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ANOVA for selected factorial modelAnalysis of variance table [Partial sum of squares - Type III]

Sum of Mean F p-value

Source Squares df Square Value Prob > F. . . .A-A 5324.51 1 5324.51 104.60 < 0.0001B-B 1820.10 1 1820.10 35.75 < 0.0001

- . . . .

BC 2482.47 1 2482.47 48.77 < 0.0001Curvature 43.69 1 43.69 0.86 0.3574

. .

Lack of Fit 3071.38 64 47.99 0.59 0.8667 Pure Error 492.00 6 82.00 Cor Total 16871.63 75

DOE Process 29

St t D li S t


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Design-Expert SoftwarePush Half-Normal Plot



A: AB: B i

99.0

99.9

F


%P

robabil

90.0

95.0 DK

FG

K: KL: L


Half-No

rm

50.0

70.0

80.0

0.0

10.0

20.0

.


0.00 9.88 19.76 29.63 39.51

DOE Process 30



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ANOVA for selected factorial modelAnalysis of variance table [Partial sum of squares - Type III]

Sum of Mean F p-value

Source S uares df S uare Value Prob > FModel 85628.80 5 17125.76 48.14 < 0.0001

D-D 14300.39 1 14300.39 40.20 < 0.0001

F-F 26366.49 1 26366.49 74.12 < 0.0001

G-G 21637.78 1 21637.78 60.83 < 0.0001K-K 5796.68 1 5796.68 16.30 0.0001

. . . .

Curvature 116.64 1 116.64 0.33 0.5688

Residual 24545.29 69 355.73. . . .

Pure Error 2391.75 6 398.63

Cor Total 1.103E+005 75

DOE Process 31



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Design-Expert SoftwareTrack Half-Normal Plot



A: AB: B i

99.0

99.9

DE


%P

robabil

90.0

95.0B

DE

L

K: KL: L


Half-No

rm

50.0

70.0

80.0

0.0

10.0

20.0

.


0.00 3.95 7.91 11.86 15.81

DOE Process 32



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ANOVA for selected factorial modelna ys s o var ance a e ar a sum o squares - ype

Sum of Mean F p-valueSource Squares df Square Value Prob > F

o e . . . < .

B-B 1388.59 1 1388.59 38.91 < 0.0001

D-D 982.81 1 982.81 27.54 < 0.0001

E-E 477.87 1 477.87 13.39 0.0005

L-L 1223.48 1 1223.48 34.28 < 0.0001

BD 2355.11 1 2355.11 65.99 < 0.0001

DE 4457.51 1 4457.51 124.90 < 0.0001

Curvature 178.00 2 89.00 2.49 0.0902

Residual 2391.15 67 35.69

Lack of Fit 1962.40 61 32.17 0.45 0.9471

Pure Error 428.75 6 71.46

DOE Process 33

.



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Burst, Maximize (LL=40, UL=65) importance ++++

= = +++, ,

Track, Minimize (LL=170, UL=200) importance +++

* Derringer, G. C., A Balancing Act: Optimizing a Product's Properties, Quality Progress. 2002 American Society for Quality

A PDF copy of this paper (with permission) is available at:

www.statease.com/pubs/derringer.pdf

DOE Process 34



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DOE Process 35


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ur a as ree par s:

. roa rus escr p on o e

planning process


3. Summary

DOE Process 36

F t i l D i Pl i P


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1. Identif o ortunit and define ob ective.

2. State objective in terms of measurable responses.

a. e ne e c ange y a s mpor an o e ec

for each response.

.

response.

.

power.

. .

the factor levels chosen determine the size ofy.)

DOE Process 37

F t i l D i Pl i P


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4. Select a desi n and:


.

Evaluate power (desire power > 80% for effects

design use only 1 ME).

xam ne e es gn ayou o ensure a e ac or

combinations are safe to run and are likely to

.

DOE Process 38

Factorial Design Planning Process Identify


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Factorial Design Planning Process IdentifyO ortunit

Tools:

Brainstorming (fishbone)

Define

Outputs Voting Form State Objective

utputs, y, , ontr ut on

Factors Voting Form

Measurable Responses

DOE inputs, levels, operating range

Other inputs

e ec npu

Factors

e ec an appropr a e ac or a es gn

Evaluate aliases (fractional factorials

and/or blocked designs)

Select

Design

va ua e power

Examine the design layoutEvaluate

Aliases & Power

DOE Process 39

Examine

Layout

Ca eat


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Caveat

power should not be applied to response surface or

Precision should be used to size response

.

Sizing for precision will covered in future

.

DOE Process 40



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Thank You f o r At t en d ingThank You f o r At t en d ing

If you have questions please email them to:

[email protected]

and reference the September 19 webinar.

DOE Process 41

9-07 factorial planning process

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