Experiments

C. F. JEFF WU, PHD, is Coca-Cola Professor in Engineering Statistics at the Georgia Institute of Technology. Dr. Wu has published more than 180 papers and is the recipient of numerous accolades, including the National Academy of Engineering membership and the COPSS Presidents' Award. MICHAEL S. HAMADA, PHD, is Senior Scientist at Los Alamos National Laboratory (LANL) in New Mexico. Dr. Hamada is a Fellow of the American Statistical Association, a LANL Fellow, and has published more than 160 papers.

• Preface to the Third Edition xviiPreface to the Second Edition xixPreface to the First Edition xxiSuggestions of Topics for Instructors xxvList of Experiments and Data Sets xxviiAbout the Companion Website xxxiii1 Basic Concepts for Experimental Design and Introductory Regression Analysis 11.1 Introduction and Historical Perspective 11.2 A Systematic Approach to the Planning and Implementation of Experiments 41.3 Fundamental Principles: Replication, Randomization, and Blocking 81.4 Simple Linear Regression 111.5 Testing of Hypothesis and Interval Estimation 141.6 Multiple Linear Regression 201.7 Variable Selection in Regression Analysis 261.8 Analysis of Air Pollution Data 281.9 Practical Summary 34Exercises 35References 432 Experiments with a Single Factor 452.1 One-Way Layout 45*2.1.1 Constraint on the Parameters 502.2 Multiple Comparisons 522.3 Quantitative Factors and Orthogonal Polynomials 562.4 Expected Mean Squares and Sample Size Determination 612.5 One-Way Random Effects Model 682.6 Residual Analysis: Assessment of Model Assumptions 712.7 Practical Summary 76Exercises 77References 823 Experiments with More than One Factor 853.1 Paired Comparison Designs 853.2 Randomized Block Designs 883.3 Two-Way Layout: Factors with Fixed Levels 923.3.1 Two Qualitative Factors: A Regression Modeling Approach 95*3.4 Two-Way Layout: Factors with Random Levels 983.5 Multi-Way Layouts 1053.6 Latin Square Designs: Two Blocking Variables 1083.7 Graeco-Latin Square Designs 112*3.8 Balanced Incomplete Block Designs 113*3.9 Split-Plot Designs 1183.10 Analysis of Covariance: Incorporating Auxiliary Information 126*3.11 Transformation of the Response 1303.12 Practical Summary 134Exercises 135Appendix 3A: Table of Latin Squares, Graeco-Latin Squares, and Hyper-Graeco-Latin Squares 147References 1484 Full Factorial Experiments at Two Levels 1514.1 An Epitaxial Layer Growth Experiment 1514.2 Full Factorial Designs at Two Levels: A General Discussion 1534.3 Factorial Effects and Plots 1574.3.1 Main Effects 1584.3.2 Interaction Effects 1594.4 Using Regression to Compute Factorial Effects 165*4.5 ANOVA Treatment of Factorial Effects 1674.6 Fundamental Principles for Factorial Effects: Effect Hierarchy, Effect Sparsity, and Effect Heredity 1684.7 Comparisons with the “One-Factor-at-a-Time” Approach 1694.8 Normal and Half-Normal Plots for Judging Effect Significance 1724.9 Lenth’s Method: Testing Effect Significance for Experiments Without Variance Estimates 1744.10 Nominal-the-Best Problem and Quadratic Loss Function 1784.11 Use of Log Sample Variance for Dispersion Analysis 1794.12 Analysis of Location and Dispersion: Revisiting the Epitaxial Layer Growth Experiment 181*4.13 Test of Variance Homogeneity and Pooled Estimate of Variance 184*4.14 Studentized Maximum Modulus Test: Testing Effect Significance for Experiments With Variance Estimates 1854.15 Blocking and Optimal Arrangement of 2k Factorial Designs in 2q Blocks 1884.16 Practical Summary 193Exercises 195Appendix 4A: Table of 2k Factorial Designs in 2q Blocks 201References 2035 Fractional Factorial Experiments at Two Levels 2055.1 A Leaf Spring Experiment 2055.2 Fractional Factorial Designs: Effect Aliasing and the Criteria of Resolution and Minimum Aberration 2065.3 Analysis of Fractional Factorial Experiments 2125.4 Techniques for Resolving the Ambiguities in Aliased Effects 2175.4.1 Fold-Over Technique for Follow-Up Experiments 2185.4.2 Optimal Design Approach for Follow-Up Experiments 2225.5 Conditional Main Effect (CME) Analysis: A Method to Unravel Aliased Interactions 2275.6 Selection of 2k−p Designs Using Minimum Aberration and Related Criteria 2325.7 Blocking in Fractional Factorial Designs 2365.8 Practical Summary 238Exercises 240Appendix 5A: Tables of 2k−p Fractional Factorial Designs 252Appendix 5B: Tables of 2k−p Fractional Factorial Designs in 2q Blocks 258References 2626 Full Factorial and Fractional Factorial Experiments at Three Levels 2656.1 A Seat-Belt Experiment 2656.2 Larger-the-Better and Smaller-the-Better Problems 2676.3 3k Full Factorial Designs 2686.4 3k−pFractional Factorial Designs 2736.5 Simple Analysis Methods: Plots and Analysis of Variance 2776.6 An Alternative Analysis Method 2826.7 Analysis Strategies for Multiple Responses I: Out-Of-Spec Probabilities 2916.8 Blocking in 3k and 3k−p Designs 2996.9 Practical Summary 301Exercises 303Appendix 6A: Tables of 3k−p Fractional Factorial Designs 309Appendix 6B: Tables of 3k−p Fractional Factorial Designs in 3q Blocks 310References 3147 Other Design and Analysis Techniques for Experiments at More than Two Levels 3157.1 A Router Bit Experiment Based on a Mixed Two-Level and Four-Level Design 3157.2 Method of Replacement and Construction of 2m4n Designs 3187.3 Minimum Aberration 2m4n Designs with n = 1, 2, 3217.4 An Analysis Strategy for 2m4n Experiments 3247.5 Analysis of the Router Bit Experiment 3267.6 A Paint Experiment Based on a Mixed Two-Level and Three-Level Design 3297.7 Design and Analysis of 36-Run Experiments at Two And Three Levels 3327.8 rk−pFractional Factorial Designs for any Prime Number r 3377.8.1 25-Run Fractional Factorial Designs at Five Levels 3377.8.2 49-Run Fractional Factorial Designs at Seven Levels 3407.8.3 General Construction 3407.9 Definitive Screening Designs 341*7.10 Related Factors: Method of Sliding Levels, Nested Effects Analysis, and Response Surface Modeling 3437.10.1 Nested Effects Modeling 3467.10.2 Analysis of Light Bulb Experiment 3477.10.3 Response Surface Modeling 3497.10.4 Symmetric and Asymmetric Relationships Between Related Factors 3527.11 Practical Summary 352Exercises 353Appendix 7A: Tables of 2m41 Minimum Aberration Designs 361Appendix 7B: Tables of 2m42 Minimum Aberration Designs 362Appendix 7C: OA(25, 56) 364Appendix 7D: OA(49, 78) 364Appendix 7E: Conference Matrices C6 C8 C10 C12 C14 and C16 366References 3688 Nonregular Designs: Construction and Properties 3698.1 Two Experiments: Weld-Repaired Castings and Blood Glucose Testing 3698.2 Some Advantages of Nonregular Designs Over the 2k−p AND 3k−p Series of Designs 3708.3 A Lemma on Orthogonal Arrays 3728.4 Plackett–Burman Designs and Hall’s Designs 3738.5 A Collection of Useful Mixed-Level Orthogonal Arrays 377*8.6 Construction of Mixed-Level Orthogonal Arrays Based on Difference Matrices 3798.6.1 General Method for Constructing Asymmetrical Orthogonal Arrays 380*8.7 Construction of Mixed-Level Orthogonal Arrays Through the Method of Replacement 3828.8 Orthogonal Main-Effect Plans Through Collapsing Factors 3848.9 Practical Summary 388Exercises 389Appendix 8A: Plackett–Burman Designs OA(N, 2N−1) with 12 ≤ N ≤ 48 and N = 4 k but not a Power of 2 394Appendix 8B: Hall’S 16-Run Orthogonal Arrays of Types II to V 397Appendix 8C: Some Useful Mixed-Level Orthogonal Arrays 399Appendix 8D: Some Useful Difference Matrices 411Appendix 8E: Some Useful Orthogonal Main-Effect Plans 413References 4149 Experiments with Complex Aliasing 4179.1 Partial Aliasing of Effects and the Alias Matrix 4179.2 Traditional Analysis Strategy: Screening Design and Main Effect Analysis 4209.3 Simplification of Complex Aliasing via Effect Sparsity 4219.4 An Analysis Strategy for Designs with Complex Aliasing 4229.4.1 Some Limitations 428*9.5 A Bayesian Variable Selection Strategy for Designs with Complex Aliasing 4299.5.1 Bayesian Model Priors 4319.5.2 Gibbs Sampling 4329.5.3 Choice of Prior Tuning Constants 4349.5.4 Blood Glucose Experiment Revisited 4359.5.5 Other Applications 437*9.6 Supersaturated Designs: Design Construction and Analysis 4379.7 Practical Summary 441Exercises 442Appendix 9A: Further Details for the Full Conditional Distributions 451References 45310 Response Surface Methodology 45510.1 A Ranitidine Separation Experiment 45510.2 Sequential Nature of Response Surface Methodology 45710.3 From First-Order Experiments to Second-Order Experiments: Steepest Ascent Search and Rectangular Grid Search 46010.3.1 Curvature Check 46010.3.2 Steepest Ascent Search 46110.3.3 Rectangular Grid Search 46610.4 Analysis of Second-Order Response Surfaces 46910.4.1 Ridge Systems 47010.5 Analysis of the Ranitidine Experiment 47210.6 Analysis Strategies for Multiple Responses II: Contour Plots and the Use of Desirability Functions 47510.7 Central Composite Designs 47810.8 Box–Behnken Designs and Uniform Shell Designs 48310.9 Practical Summary 486Exercises 488Appendix 10A: Table of Central Composite Designs 498Appendix 10B: Table of Box–Behnken Designs 500Appendix 10C: Table of Uniform Shell Designs 501References 50211 Introduction to Robust Parameter Design 50311.1 A Robust Parameter Design Perspective of the Layer Growth and Leaf Spring Experiments 50311.1.1 Layer Growth Experiment Revisited 50311.1.2 Leaf Spring Experiment Revisited 50411.2 Strategies for Reducing Variation 50611.3 Noise (Hard-to-Control) Factors 50811.4 Variation Reduction Through Robust Parameter Design 51011.5 Experimentation and Modeling Strategies I: Cross Array 51211.5.1 Location and Dispersion Modeling 51311.5.2 Response Modeling 51811.6 Experimentation and Modeling Strategies II: Single Array and Response Modeling 52311.7 Cross Arrays: Estimation Capacity and Optimal Selection 52611.8 Choosing Between Cross Arrays and Single Arrays 529*11.8.1 Compound Noise Factor 53311.9 Signal-to-Noise Ratio and Its Limitations for Parameter Design Optimization 53411.9.1 SN Ratio Analysis of Layer Growth Experiment 536*11.10 Further Topics 53711.11 Practical Summary 539Exercises 541References 55012 Analysis of Experiments with Nonnormal Data 55312.1 A Wave Soldering Experiment with Count Data 55312.2 Generalized Linear Models 55412.2.1 The Distribution of the Response 55512.2.2 The Form of the Systematic Effects 55712.2.3 GLM versus Transforming the Response 55812.3 Likelihood-Based Analysis of Generalized Linear Models 55812.4 Likelihood-Based Analysis of theWave Soldering Experiment 56212.5 Bayesian Analysis of Generalized Linear Models 56412.6 Bayesian Analysis of the Wave Soldering Experiment 56512.7 Other Uses and Extensions of Generalized Linear Models and Regression Models for Nonnormal Data 567*12.8 Modeling and Analysis for Ordinal Data 56712.8.1 The Gibbs Sampler for Ordinal Data 569*12.9 Analysis of Foam Molding Experiment 57212.10 Scoring: A Simple Method for Analyzing Ordinal Data 57512.11 Practical Summary 576Exercises 577References 58713 Practical Optimal Design 58913.1 Introduction 58913.2 A Design Criterion 59013.3 Continuous and Exact Design 59013.4 Some Design Criteria 59213.4.1 Nonlinear Regression Model, Generalized Linear Model, and Bayesian Criteria 59313.5 Design Algorithms 59513.5.1 Point Exchange Algorithm 59513.5.2 Coordinate Exchange Algorithm 59613.5.3 Point and Coordinate Exchange Algorithms for Bayesian Designs 59613.5.4 Some Design Software 59713.5.5 Some Practical Considerations 59713.6 Examples 59813.6.1 A Quadratic Regression Model in One Factor 59813.6.2 Handling a Constrained Design Region 59813.6.3 Augmenting an Existing Design 59813.6.4 Handling an Odd-Sized Run Size 60013.6.5 Blocking from Initially Running a Subset of a Designed Experiment 60113.6.6 A Nonlinear Regression Model 60513.6.7 A Generalized Linear Model 60513.7 Practical Summary 606Exercises 607References 60814 Computer Experiments 61114.1 An Airfoil Simulation Experiment 61114.2 Latin Hypercube Designs (LHDs) 61314.2.1 Orthogonal Array-Based Latin Hypercube Designs 61714.3 Latin Hypercube Designs with Maximin Distance or Maximum Projection Properties 61914.4 Kriging: The Gaussian Process Model 62214.5 Kriging: Prediction and Uncertainty Quantification 62514.5.1 Known Model Parameters 62614.5.2 Unknown Model Parameters 62714.5.3 Analysis of Airfoil Simulation Experiment 62914.6 Expected Improvement 63114.6.1 Optimization of Airfoil Simulation Experiment 63314.7 Further Topics 63414.8 Practical Summary 636Exercises 637Appendix 14A: Derivation of the Kriging Equations (14.10) and (14.11) 643Appendix 14B: Derivation of the EI Criterion (14.22) 644 References 645Appendix A Upper Tail Probabilities of the Standard Normal Distribution ∫ ∞z 1/√2𝜋e−u2∕2du 647Appendix B Upper Percentiles of the t Distribution 649Appendix C Upper Percentiles of the 𝜒 2 Distribution 651Appendix D Upper Percentiles of the F Distribution 653Appendix E Upper Percentiles of the Studentized Range Distribution 661Appendix F Upper Percentiles of the Studentized Maximum Modulus Distribution 669Appendix G Coefficients of Orthogonal Contrast Vectors 683Appendix H Critical Values for Lenth’s Method 685Author Index 689Subject Index 693