9-07 factorial planning process
TRANSCRIPT
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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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Factorial Design Planning Process (2 of 2)
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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Factorial Design Planning Process
ur a as ree par s:
. roa rus escr p on o e
planning process
2. Illustrate key points via an example
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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Stent Delivery System
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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Stent Delivery System
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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Stent Delivery System
.
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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Stent Delivery System
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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Stent Delivery System
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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Stent Delivery System
4. Select a desi n want resolution V:
Evaluate aliases (fractional factorials and/or
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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Stent Delivery System
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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Stent Delivery System
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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Stent Delivery System
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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Stent Delivery System
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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Stent Delivery System
Design-Expert SoftwarePush Half-Normal Plot
Error from replicates
Shapiro-Wilk testW-value = 0.993p-value = 0.978
A: AB: B i
99.0
99.9
F
C: CD: DE: EF: FG: GH: HJ: J l
%P
robabil
90.0
95.0 DK
FG
K: KL: L
Positive EffectsNegative Effects
Half-No
rm
50.0
70.0
80.0
0.0
10.0
20.0
.
|Standardized Effect|
0.00 9.88 19.76 29.63 39.51
DOE Process 30
Stent Delivery System
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Stent Delivery System
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
Stent Delivery System
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Stent Delivery System
Design-Expert SoftwareTrack Half-Normal Plot
Error from replicates
Shapiro-Wilk testW-value = 0.972p-value = 0.181
A: AB: B i
99.0
99.9
DE
C: CD: DE: EF: FG: GH: HJ: J l
%P
robabil
90.0
95.0B
DE
L
K: KL: L
Positive EffectsNegative Effects
Half-No
rm
50.0
70.0
80.0
0.0
10.0
20.0
.
|Standardized Effect|
0.00 3.95 7.91 11.86 15.81
DOE Process 32
Stent Delivery System
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Stent Delivery System
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
.
Stent Delivery System
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Stent Delivery System
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
Stent Delivery System
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Stent Delivery System
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Factorial Design Planning Process
ur a as ree par s:
. roa rus escr p on o e
planning process
2. Illustrate key points via an example
3. Summary
DOE Process 36
F t i l D i Pl i P
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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 37
F t i l D i Pl i P
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Factorial Design Planning Process (2 of 2)
4. Select a desi n and:
Evaluate aliases (fractional factorials and/or
.
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
Factorial Design Planning Process
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Factorial Design Planning Process
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:
and reference the September 19 webinar.
DOE Process 41