Design of Experiments - US Army Conference on Applied Statistics

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The Model/<strong>Design</strong> Relationship – Predicted Responses The predicted values <strong>of</strong> the response are contained in the vector: Where the so-called, “hat” matrix, H, is: The variance matrix <strong>of</strong> the predicted responses is: Again, is inherent to the system, but we choose the design, X.
The Model/<strong>Design</strong> Relationship – Aliasing Suppose the best polynomial approximating model is: But we estimate only 1 using least-squares: Now the elements <strong>of</strong> the least-squares estimates <strong>of</strong> 1 are biased by 2 , that is: where the alias matrix, A, is:
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: 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 and 58: Stepwise Fit Response: Shrinkage St
Page 59 and 60: No-Confounding Design</stro
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
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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
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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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