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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    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

    DOE Process 35

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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:

    [email protected]

    and reference the September 19 webinar.

    DOE Process 41