Design of Experiments - US Army Conference on Applied Statistics

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Scenario Suppose we are testing a system with 10 components. For simplicity, let each component have two settings. (This constraint can be relaxed) We want to make sure that each pair <strong>of</strong> components has all 4 possible combinations tested. We want to perform as few system tests as possible. (Guess the minimum number <strong>of</strong> necessary tests) Note: it is not necessary to fit a model – just demonstrate that pairwise combinations work
Covering Array Definition A covering array CA(N; t, k, v) is an N k array such that the i-th column contains v distinct symbols. If a CA(N; t, k, v) has the property that for any t coordinate projection, all v t combinations <strong>of</strong> symbols exist, then it is a t-covering array (or strength t covering array). A t-covering array is optimal if N is minimal for fixed t, k, and v. N is the number <strong>of</strong> tests. (find minimum N) k is the number <strong>of</strong> factors. (k=10) t is the number <strong>of</strong> factors such that all t-factor combinations are tested. (t=2) v is the number <strong>of</strong> levels <strong>of</strong> each factor. (v=2)
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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
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The data for the example came from
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Embarrassing Problem Case Suppose w
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Reactor Case Study Box, Hunter and
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Robust Screening Design</st
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Robust Screening Design</st
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The Case for Non-orthogonal <strong
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References Hall, M. Jr. (1961). Had
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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
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 142 and 143: Response Surface Methodology • Wh
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: • Goals Module 10 - Covering Arra
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
Page 193 and 194: CA(N:2,k,2) Results k 2-3 4 5-10 11
Page 195 and 196: References • R. Brownlie, J. Prow
Page 197 and 198: Module 10 - Summary • Covering ar
Page 199 and 200: 199 What is a supersaturated design
Page 201 and 202: 201 A more general definition… Su
Page 203 and 204: 203 Classical “supersaturated”
Page 205 and 206: 205 Case 2 - Fractional Factorial <
Page 207 and 208: 207 Problem D-Optimal designs depen
Page 209 and 210: 209 Example 2 6-2 Fractional Factor
Page 211 and 212: 211 Bayesian D-Optimal designs Find
Page 213 and 214: 213 Question Why should only higher
Page 215 and 216: Card Trick in JMP
Page 217: DOX Course - Final Thoughts 1. Opti
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Design of Experiments - US Army Conference on Applied Statistics

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