Experiments: Planning, Analysis, and Optimization

Preface to the Third Edition Preface to the Second Edition xvii Preface to the First Edition xix Suggestions of Topics for Instructors xxiii List of Experiments and Data Sets xxv 1 Basic Concepts for Experimental Design and IntroductoryRegression Analysis 1.1 Introduction and Historical Perspective, 1 1.2 A Systematic Approach to the Planning and Implementationof Experiments, 4. 1.3 Fundamental Principles: Replication, Randomization,and Blocking, 8. 1.4 Simple Linear Regression, 11. 1.5 Testing of Hypothesis and Interval Estimation, 14. 1.6 Multiple Linear Regression, 20 1.7 Variable Selection in Regression Analysis, 26 1.8 Analysis of Air Pollution Data, 29 1.9 Practical Summary, 34 Exercises, 36 References, 43 2 Experiments with a Single Factor 45 2.1 One-Way Layout, 45 *2.1.1 Constraint on the Parameters, 50 2.2 Multiple Comparisons, 53 2.3 Quantitative Factors and Orthogonal Polynomials, 57 2.4 Expected Mean Squares and Sample Size Determination, 63 2.5 One-Way Random Effects Model, 70 2.6 Residual Analysis: Assessment of Model Assumptions, 74 2.7 Practical Summary, 79 Exercises, 80 References, 86 3 Experiments with More Than One Factor 87 3.1 Paired Comparison Designs, 87 3.2 Randomized Block Designs, 90 3.3 Two-Way Layout: Factors with Fixed Levels, 94 3.3.1 Two Qualitative Factors: A Regression ModelingApproach, 97 *3.4 Two-Way Layout: Factors with Random Levels, 99 3.5 Multi-Way Layouts, 108 3.6 Latin Square Designs: Two Blocking Variables, 110 3.7 Graeco-Latin Square Designs, 114 *3.8 Balanced Incomplete Block Designs, 115 *3.9 Split-Plot Designs, 120 3.10 Analysis of Covariance: Incorporating AuxiliaryInformation, 128 *3.11 Transformation of the Response, 133 3.12 Practical Summary, 137 Exercises, 138 Appendix 3A: Table of Latin Squares, Graeco-Latin Squares, andHyper-Graeco-Latin Squares, 150 References, 152 4 Full Factorial Experiments at Two Levels155 4.1 An Epitaxial Layer Growth Experiment, 155 4.2 Full Factorial Designs at Two Levels: A General Discussion, 157 4.3 Factorial Effects and Plots, 161 4.3.1 Main Effects, 162 4.3.2 Interaction Effects, 164 4.4 Using Regression to Compute Factorial Effects, 169 *4.5 ANOVA Treatment of Factorial Effects, 171 4.6 Fundamental Principles for Factorial Effects: Effect Hierarchy,Effect Sparsity, and Effect Heredity, 172 4.7 Comparisons with the "One-Factor-at-a-Time" Approach, 173 4.8 Normal and Half-Normal Plots for Judging EffectSignificance, 177 4.9 Lenth's Method: Testing Effect Significance for Experimentswithout Variance Estimates, 180 4.10 Nominal-the-Best Problem and Quadratic LossFunction, 183 4.11 Use of Log Sample Variance for Dispersion Analysis, 184 4.12 Analysis of Location and Dispersion: Revisiting the EpitaxialLayer Growth Experiment, 185 *4.13 Test of Variance Homogeneity and Pooled Estimate ofVariance, 188* 4.14 Studentized Maximum Modulus Test: Testing Effect Significancefor Experiments with Variance Estimates, 190 4.1 5Blocking and Optimal Arrangement of 2kFactorial Designs in 2qBlocks, 193 4.16 Practical Summary, 198 Exercises, 200 Appendix 4A: Table of 2kFactorial Designs in 2qBlocks, 207 References, 208 5 Fractional Factorial Experiments at Two Levels 211 5.1 A Leaf Spring Experiment, 211 5.2 Fractional Factorial Designs: Effect Aliasing and the Criteria ofResolution and Minimum Aberration, 213 5.3 Analysis of Fractional Factorial Experiments, 219 5.4 Techniques for Resolving the Ambiguities in Aliased Effects, 225 5.4.1 Fold-Over Technique for Follow-Up Experiments, 225 5.4.2 Optimal Design Approach for Follow-UpExperiments, 229 5.5 CME 5.6 Selection of 2k.pDesigns Using Minimum Aberration and RelatedCriteria, 234 5.7Blocking in Fractional Factorial Designs, 238 5.8Practical Summary, 240 Exercises, 242 Appendix 5A: Tables of 2k.pFractional Factorial Designs, 252 Appendix 5B: Tables of 2k.pFractional Factorial Designs in 2qBlocks, 260 References, 264 6 Full Factorial and Fractional Factorial Experiments at ThreeLevels267 6.1A Seat-Belt Experiment, 267 6.2 Larger-the-Better and Smaller-the-Better Problems, 268 6.3 3kFull Factorial Designs, 270 6.4 3k.pFractional Factorial Designs, 275 6.5 Simple Analysis Methods: Plots and Analysis of Variance, 279 6.6 An Alternative Analysis Method, 287 6.7Analysis Strategies for Multiple Responses I: Out-of-SpecProbabilities, 293 6.8 Blocking in 3kand 3k.pDesigns, 302 6.9 Practical Summary, 303 Exercises, 305 Appendix 6A: Tables of 3k.pFractional Factorial Designs, 312 Appendix 6B: Tables of 3k.pFractional Factorial Designs in 3qBlocks, 313 References, 317 7 Other Design and Analysis Techniques for Experiments atMore Than Two Levels319 7.1A Router Bit Experiment Based on a Mixed Two-Level andFour-Level Design, 319 7.2Method of Replacement and Construction of 2m4nDesigns, 322 7.3Minimum Aberration 2m4nDesigns withn=1,2, 325 7.4An Analysis Strategy for 2m4nExperiments, 328 7.5Analysis of the Router Bit Experiment, 330 7.6A Paint Experiment Based on a Mixed Two-Level and Three-LevelDesign, 334 7.7Design and Analysis of 36-Run Experiments at Two and ThreeLevels, 334 7.8rk.pFractional Factorial Designs for any Prime Numberr, 341 7.8.125-Run Fractional Factorial Designs at Five Levels, 342 7.8.249-Run Fractional Factorial Designs at Seven Levels, 345 7.8.3General Construction, 345 7.9 DSD *7.10Related Factors: Method of Sliding Levels, Nested EffectsAnalysis, and Response Surface Modeling, 346 7.10.1Nested Effects Modeling, 348 7.10.2Analysis of Light Bulb Experiment, 350 7.10.3Response Surface Modeling, 353 7.10.4Symmetric and Asymmetric Relationships BetweenRelated Factors, 355 7.11Practical Summary, 356 Exercises, 357 Appendix 7A: Tables of 2m41Minimum Aberration Designs, 364 Appendix 7B: Tables of 2m42Minimum Aberration Designs, 366 Appendix 7C: OA(25, 56), 368 Appendix 7D: OA(49, 78), 368 Appendix 7E: Conference Matrices References, 370 8Nonregular Designs: Construction and Properties371 8.1Two Experiments: Weld-Repaired Castings and Blood GlucoseTesting, 371 8.2Some Advantages of Nonregular Designs Over the 2k.pand 3k.pSeries of Designs, 373 8.3A Lemma on Orthogonal Arrays, 374 8.4Plackett - Burman Designs and Hall's Designs, 375 8.5A Collection of Useful Mixed-Level Orthogonal Arrays, 379 *8.6Construction of Mixed-Level Orthogonal Arrays Based onDifference Matrices, 381 8.6.1General Method for Constructing AsymmetricalOrthogonal Arrays, 382* 8.7Construction of Mixed-Level Orthogonal Arrays Through theMethod of Replacement, 384 8.8Orthogonal Main-Effect Plans Through Collapsing Factors, 386 8.9Practical Summary, 390 Exercises, 391 Appendix 8A: Plackett - Burman Designs OA(N,2N.1)with 12<=N<=48andN=4kBut Not a Power of 2, 397 Appendix 8B: Hall's 16-Run Orthogonal Arrays of Types II to V, 401 Appendix 8C: Some Useful Mixed-Level Orthogonal Arrays, 405 Appendix 8D: Some Useful Difference Matrices, 416 Appendix 8E: Some Useful Orthogonal Main-Effect Plans, 418 References, 419 9Experiments with Complex Aliasing421 9.1Partial Aliasing of Effects and the Alias Matrix, 421 9.2Traditional Analysis Strategy:Screening Design and Main EffectAnalysis, 424 9.3Simplification of Complex Aliasing via Effect Sparsity, 424 9.4An Analysis Strategy for Designs with Complex Aliasing, 426 9.4.1Some Limitations, 432 *9.5A Bayesian Variable Selection Strategy for Designswith Complex Aliasing, 433 9.5.1Bayesian Model Priors, 435 9.5.2Gibbs Sampling, 437 9.5.3Choice of Prior Tuning Constants, 438 9.5.4Blood Glucose Experiment Revisited, 439 9.5.5Other Applications, 441 *9.6Supersaturated Designs: Design Constructionand Analysis, 442 9.7Practical Summary, 445 Exercises, 446 Appendix 9A: Further Details for the Full Conditional Distributions, 454 References, 456 10 Response Surface Methodology459 10.1A Ranitidine Separation Experiment, 459 10.2Sequential Nature of Response SurfaceMethodology, 461 10.3From First-Order Experiments to Second-Order Experiments:Steepest Ascent Search and Rectangular Grid Search, 464 10.3.1Curvature Check, 465 10.3.2Steepest Ascent Search, 466 10.3.3Rectangular Grid Search, 470 10.4Analysis of Second-Order Response Surfaces, 473 10.4.1Ridge Systems, 475 10.5Analysis of the Ranitidine Experiment, 477 10.6Analysis Strategies for Multiple Responses II: Contour Plotsand the Use of Desirability Functions, 481 10.7Central Composite Designs, 484 10.8Box - Behnken Designs and Uniform Shell Designs, 489 10.9Practical Summary, 492 Exercises, 494 Appendix 10A: Table of Central Composite Designs, 505 Appendix 10B: Table of Box - Behnken Designs, 507 Appendix 10C: Table of Uniform Shell Designs, 508 References, 509 11 Introduction to Robust Parameter Design511 11.1 A Robust Parameter Design Perspective of the Layer Growthand Leaf Spring Experiments, 511 11.1.1 Layer Growth Experiment Revisited, 511 11.1.2 Leaf Spring Experiment Revisited, 512 11.2 Strategies for Reducing Variation, 514 11.3 Noise (Hard-to-Control) Factors, 516 11.4 Variation Reduction Through Robust Parameter Design, 518 11.5 Experimentation and Modeling Strategies I:Cross Array, 520 11.5.1 Location and Dispersion Modeling, 52 111.5.2 Response Modeling, 526 11.6 Experimentation and Modeling Strategies II: Single Array andResponse Modeling, 532 11.7 Cross Arrays: Estimation Capacity and Optimal Selection, 535 11.8 Choosing Between Cross Arrays and Single Arrays, 538 *11.8.1 Compound Noise Factor, 542 11.9 Signal-to-Noise Ratio and Its Limitations for Parameter DesignOptimization, 543 11.9.1 SN Ratio Analysis of Layer Growth Experiment, 546* 11.10 Further Topics, 547 11.11 Practical Summary, 548 Exercises, 550 References, 560 12 Analysis of Experiments with Nonnormal Data625 12.1 A Wave Soldering Experiment with Count Data, 625 12.2 Generalized Linear Models, 627 12.2.1 The Distribution of the Response, 627 12.2.2 The Form of the Systematic Effects, 629 12.2.3 GLM versus Transforming the Response, 630 12.3 Likelihood-Based Analysis of Generalized Linear Models, 631 [New equations for Section 12.3 in Word file 'Add to Section 12.3] 12.4 Likelihood-Based Analysis of the Wave SolderingExperiment, 634 12.5 Bayesian Analysis of Generalized Linear Models, 635 12.6 Bayesian Analysis of the Wave Soldering Experiment, 637 12.7 Other Uses and Extensions of Generalized Linear Models andRegression Models for Nonnormal Data, 639 *12.8 Modeling and Analysis for Ordinal Data, 639 12.8.1The Gibbs Sampler for Ordinal Data, 642 *12.9 Analysis of Foam Molding Experiment, 644 12.10 Scoring: A Simple Method for Analyzing Ordinal Data, 647 12.11 Practical Summary, 649 Exercises, 649 References, 661 13. [Insert 'New Chapter_POD'] 14. [Insert 'New Chapter 14_CE'] Appendix A Upper Tail Probabilities of the Standard NormalDistribution, integral infinity z1 square root 2pie.u2/2du663 Appendix B Upper Percentiles of thetDistribution665 Appendix C Upper Percentiles of thechi2Distribution667 Appendix D Upper Percentiles of theFDistribution669 Appendix E Upper Percentiles of the Studentized RangeDistribution677 Appendix F Upper Percentiles of the Studentized MaximumModulus Distribution685 Appendix G Coefficients of Orthogonal Contrast Vectors699 Appendix H Critical Values for Lenth's Method701 Author Index705 Subject Index 709