Design of Experiments - US Army Conference on Applied Statistics

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Stepwise Fit Response: Shrinkage Stepwise Regression Control Prob to Enter Prob to Leave Direction:Forward 0.250 0.100 Rules: Combine Current Estimates SSE 133.18753 DFE 10 LockEntered Parameter Intercept A B C D E F A*B A*C A*D A*E A*F B*C B*D B*E B*F C*D C*E C*F D*E D*F E*F Step History Step 1 2 Parameter A*B A*D MSE 13.318753 Action Entered Entered RSquare 0.9800 Estimate 27.3125 6.9375 17.8125 0 -4.441e-16 0 0 5.9375 0 -2.6875 0 0 0 0 0 0 0 0 0 0 0 0 nDF 1 3 2 1 2 1 1 1 2 1 2 2 2 1 2 2 2 3 3 2 2 3 "Sig Prob" 0.0000 0.0440 RSquare Adj 0.9700 SS 0 1449.688 5640.625 3.16e-30 115.5625 4.21e-30 4.21e-30 564.0625 11.39834 115.5625 26.80068 13.7383 1.58e-29 11.39834 13.7383 26.80068 13.78835 1.933557 31.4007 31.4007 1.933557 2.459758 Seq SS 6410.688 115.5625 "F Ratio" 0.000 36.282 211.755 0.000 4.338 0.000 0.000 42.351 0.374 8.677 1.008 0.460 0.000 0.842 0.460 1.008 0.462 0.034 0.720 1.234 0.059 0.044 RSquare 0.9626 0.9800 Cp . AIC 45.90671 "Prob>F" 1.0000 0.0000 0.0000 1.0000 0.0440 1.0000 1.0000 0.0001 0.6992 0.0146 0.4071 0.6470 1.0000 0.3827 0.6470 0.4071 0.6459 0.9907 0.5711 0.3411 0.9432 0.9867 Cp . . p 4 6 Stepwise regression selects the main effects <strong>of</strong> A and B, along with the AB and AD interactions The main effect <strong>of</strong> D is added to preserve the hierarchy in the model The no-confounding design correctly identifies the model without any ambiguity and no need for additional runs 58
No-Confounding <strong>Design</strong>s • The 16-run minimum aberration resolution IV designs (6, 7, and 8 factors) are among the most widely used designs in practice • It is possible to find no-confounding designs that are superior to the standard minimum aberration resolution IV designs in the sense that they <strong>of</strong>fer a better chance <strong>of</strong> detecting significant two-factor interactions • These designs are constructed from the Hall matrices 59
Page 1 and 2:
Design of<
Page 3 and 4:
What Is a Designed
Page 5 and 6:
What Is a Response? A response is a
Page 7 and 8: What is a model? a simplified mathe
Page 9 and 10: Important Points from the Fathers <
Page 11 and 12: ANOVA Model for Mileage Study Note
Page 13 and 14: Orthogonal Coding and Orthogonal <s
Page 15 and 16: ANOVA/Regression Model - Matrix Not
Page 17 and 18: Categorical Factor Coding - 2 level
Page 19 and 20: Continuous Factor Coding MR - midra
Page 21 and 22: The Model/Design R
Page 23 and 24: The Model/Design R
Page 25 and 26: Design Optimality
Page 27 and 28: Simple experiment for three factors
Page 29 and 30: Standard designs using an optimal d
Page 31 and 32: INPUTS (Factors) Airspeed Turn Rate
Page 33 and 34: Fractional Factorial designs are D-
Page 35: Consider the 2 5-1 - Again Created
Page 38 and 39: JMP Demo Relative Variance
Page 40 and 41: INPUTS (Factors) 40 SPEAR AGM Tests
Page 42 and 43: Suppose that we want to focus on ma
Page 44 and 45: Alias Matrix Effect Intercept A B C
Page 46 and 47: Module 2 - Summary 1. Main message
Page 48 and 49: Regular Designs ma
Page 50 and 51: Define Nonisomorphic Two designs ar
Page 53 and 54: Screening for Shrinkage Contrasts T
Page 55 and 56: Where Did the Data in this Experime
Page 57: Stepwise Fit Response: Shrinkage St
Page 61 and 62: Hall II 15 Factor Design</s
Page 63 and 64: Hall IV 15 Factor Design</s
Page 65 and 66: Constructing the Recommended 6 Fact
Page 67 and 68: Color Plot for the Standard Minimum
Page 69 and 70: Recommended Nonregular 7 Factor <st
Page 71 and 72: Color Plot for the Standard Minimum
Page 73 and 74: Recommended Nonregular 8 Factor <st
Page 75 and 76: Alternatives to Resolution III <str
Page 77 and 78: Recommended 10 Factor Desig
Page 83 and 84: Note that both main effects and two
Page 85 and 86: Main effects are not aliased. One t
Page 87 and 88: Plackett-Burman Design</str
Page 89: A 12-Factor Example 1 1 1 1 1 1 1 1
Page 92 and 93: The data for the example came from
Page 94 and 95: Embarrassing Problem Case Suppose w
Page 96 and 97: Reactor Case Study Box, Hunter and
Page 98 and 99: Robust Screening Design</st
Page 100 and 101: Robust Screening Design</st
Page 102 and 103: The Case for Non-orthogonal <strong
Page 104 and 105: References Hall, M. Jr. (1961). Had
Page 106 and 107: Module 4 - Blocking • Many experi
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Blocking • Blocking is a techniqu
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The randomized complete block desig
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Cars The Latin Square Desig
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JMP Demo
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Another Example of
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In general, if there are p treatmen
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Back to tire testing • Suppose th
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Module 4 - Summary • Most design
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Split-plot Graphic Definition
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Model for Split-plot Experi
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General procedure Split-plot <stron
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Scenario 1. Four factors Split-Plot
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Ad hoc Design #1
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I-optimal Split-Plot Design
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OLS vs GLS Data Analysis OLS Analys
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Module 6 - Introduction to RSM •
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E(y) = f( ) The response surface Th
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Response Surface Methodology • Wh
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CI on the mean response at a point
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Three Typical Applications
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Useful References on RSM • Box, G
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Categorical and Continuous Variable
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Goals Module 7 - RSM with Factor Co
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A problem with a constrained design
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JMP Default RSM Design</str
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Design Comparison
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Module 7 - Summary • Constraints
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Robust Parameter Design</st
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The Response Surface Approach Secti
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Filtration Robust Processing Exampl
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JMP Demo
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• Goals Module 9 Mixture
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Mixtures occur in lots of</
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Simplex Designs Si
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An experiment involving shampoo for
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Makeup of an Aircr
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Mixtures in JMP Ternary Plot .1 X1
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• Goals Module 10 - Covering Arra
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Covering Array Definition A coverin
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Covering arrays 1 1 1 1 1 2 2 2 2 2
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Covering arrays and sof</st
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Example - Air to ground missile sys
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CA(N:2,k,2) Results k 2-3 4 5-10 11
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References • R. Brownlie, J. Prow
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Module 10 - Summary • Covering ar
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199 What is a supersaturated design
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201 A more general definition… Su
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203 Classical “supersaturated”
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205 Case 2 - Fractional Factorial <
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207 Problem D-Optimal designs depen
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209 Example 2 6-2 Fractional Factor
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211 Bayesian D-Optimal designs Find
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213 Question Why should only higher
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Card Trick in JMP
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DOX Course - Final Thoughts 1. Opti
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Design of Experiments - US Army Conference on Applied Statistics

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