Design of Experiments - US Army Conference on Applied Statistics

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Response Surface Methodology • Why do we use second-order models in RSM? • They are flexible • It is easy to estimate the parameters • There is a lot <strong>of</strong> empirical evidence that they work • Philosophy <strong>of</strong> using low-order polynomials is based on a Taylor series analogy
Confidence Intervals (Page 36) CI on individual model parameter: b t se( b ) b t se( b ) j / 2, n p j j j / 2, n p j Joint confidence region on model parameters: (b - β) X X(b - β) F Elliptically-shaped region , p, n p pMS E Tricky to construct Conceptually very useful
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Design of<
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What Is a Designed
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What Is a Response? A response is a
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What is a model? a simplified mathe
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Important Points from the Fathers <
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ANOVA Model for Mileage Study Note
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Orthogonal Coding and Orthogonal <s
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ANOVA/Regression Model - Matrix Not
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Categorical Factor Coding - 2 level
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Continuous Factor Coding MR - midra
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The Model/Design R
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The Model/Design R
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Design Optimality
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Simple experiment for three factors
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Standard designs using an optimal d
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INPUTS (Factors) Airspeed Turn Rate
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Fractional Factorial designs are D-
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Consider the 2 5-1 - Again Created
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JMP Demo Relative Variance
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INPUTS (Factors) 40 SPEAR AGM Tests
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Suppose that we want to focus on ma
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Alias Matrix Effect Intercept A B C
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Module 2 - Summary 1. Main message
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Regular Designs ma
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Define Nonisomorphic Two designs ar
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Screening for Shrinkage Contrasts T
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Where Did the Data in this Experime
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Stepwise Fit Response: Shrinkage St
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No-Confounding Design</stro
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Hall II 15 Factor Design</s
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Hall IV 15 Factor Design</s
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Constructing the Recommended 6 Fact
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Color Plot for the Standard Minimum
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Recommended Nonregular 7 Factor <st
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Color Plot for the Standard Minimum
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Recommended Nonregular 8 Factor <st
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Alternatives to Resolution III <str
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Recommended 10 Factor Desig
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Note that both main effects and two
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Main effects are not aliased. One t
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Plackett-Burman Design</str
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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
Page 108 and 109: Blocking • Blocking is a techniqu
Page 110 and 111: The randomized complete block desig
Page 112 and 113: Cars The Latin Square Desig
Page 114 and 115: JMP Demo
Page 116 and 117: Another Example of
Page 118 and 119: In general, if there are p treatmen
Page 120 and 121: Back to tire testing • Suppose th
Page 122 and 123: Module 4 - Summary • Most design
Page 124 and 125: Split-plot Graphic Definition
Page 126 and 127: Model for Split-plot Experi
Page 128 and 129: General procedure Split-plot <stron
Page 130 and 131: Scenario 1. Four factors Split-Plot
Page 132 and 133: Ad hoc Design #1
Page 134 and 135: I-optimal Split-Plot Design
Page 136 and 137: OLS vs GLS Data Analysis OLS Analys
Page 138 and 139: Module 6 - Introduction to RSM •
Page 140 and 141: E(y) = f( ) The response surface Th
Page 144 and 145: CI on the mean response at a point
Page 147 and 148: Three Typical Applications
Page 149 and 150: Useful References on RSM • Box, G
Page 151 and 152: Categorical and Continuous Variable
Page 153 and 154: Goals Module 7 - RSM with Factor Co
Page 155 and 156: A problem with a constrained design
Page 157 and 158: JMP Default RSM Design</str
Page 159 and 160: Design Comparison
Page 161 and 162: Module 7 - Summary • Constraints
Page 163 and 164: Robust Parameter Design</st
Page 165 and 166: The Response Surface Approach Secti
Page 167 and 168: Filtration Robust Processing Exampl
Page 169 and 170: JMP Demo
Page 171 and 172: • Goals Module 9 Mixture
Page 173 and 174: Mixtures occur in lots of</
Page 175 and 176: Simplex Designs Si
Page 177 and 178: An experiment involving shampoo for
Page 179 and 180: Makeup of an Aircr
Page 181 and 182: Mixtures in JMP Ternary Plot .1 X1
Page 183 and 184: • Goals Module 10 - Covering Arra
Page 185 and 186: Covering Array Definition A coverin
Page 187 and 188: Covering arrays 1 1 1 1 1 2 2 2 2 2
Page 189 and 190: Covering arrays and sof</st
Page 191 and 192: 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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