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Completely revised and expanded, this Third Edition maintains a balance between design and analysis topics, but includes new material and numerous updated examples. Added, expanded and reorganized chapters provide more in-depth treatment of 2^k factorial and fractional factorial designs; brand new topical coverage of factorial and fractional factorial design; a discussion of the Taguchi approach to parameter design, along with a critique of this method and recommended alternatives; additional topics on the selection of a response surface design; and an introduction to the mixture problem. Throughout, it stresses the importance of experimental design (as a tool for the practicing engineer) to product design and development, process development and improvement and process troubleshooting.

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CONTENTS
Chapter 1. Introduction = 1
  1-1 What is Experimental Design? = 1
  1-2 Applications of Experimental Design = 3
  1-3 Basic Principles = 8
  1-4 Guidelines for Designing Experiments = 9
  1-5 Historical Perspective = 12
  1-6 Using Statistical Techniques in Experimentation = 12
Chapter 2. Simple comparative Experiments = 14
  2-1 Intorduction = 14
  2-2 Basic Statistical Concepts = 15
  2-3 Sampling and Sampling Distributions = 20
  2-4 Inferences About the Differences in Means, Randomized Designs = 27
    2-4.1 Hypothesis Testing = 28
    2-4.2 Choice of Sample Size = 31
    2-4.3 Confidence Intervals = 33
    2-4.4 The Case Where σ1 2 ≠ σ2 2 = 34
    2-4.5 The Case Where σ1 2 and σ2 2 Are Known = 35
    2-4.6 Comparing a Single Mean to a Specified Value = 36
    2-4.7 Summary = 37
  2-5 Inferences About the Difference in Means, Paired Comparison Designs = 38
    2-5.1 The Paired Comparison Problem = 38
    2-5.2 Advantages of the paired Comparison Design = 41
  2-6 Inferences About the Variances of Normal Distributions = 42
  2-7 Problems = 45
Chapter 3. Experiments with a Single factor : The Analysis of Variance = 50
  3-1 An Example = 51
  3-2 The Analysis of Variance = 53
  3-3 Analysis of the Fixed Effects Model = 55
    3-3.1 Decomposition of the Total Sum of Squares = 55
    3-3.2 Statistical Analysis = 59
    3-3.3 Estimation of the Model Parameters = 63
    3-3.4 Model Adequacy Checking : Preview = 66
    3-3.5 The Unbalanced Case = 67
  3-4 Comparison of Individual Treatment Means = 67
    3-4.1 Graphical Comparison of Means = 67
    3-4.2 Contrasts = 69
    3-4.3 Orthogonal Contrasts = 70
    3-4.4 Scheff e ´ 's Method for comparing All Contrasts = 72
    3-4.5 Comparing Pairs of Treatment Means = 73
    3-4.6 Comparing Treatments with a Control = 79
  3-5 The Random Effects Model = 81
  3-6 Sample Computer Output = 87
  3-7 Problems = 87
Chapter 4. More About Single-Factor Experiments = 95
  4-1 Model Adequacy Checking = 95
    4-1.1 The Normality Assumption = 96
    4-1.2 Plot of Residuals in time Sequence = 99
    4-1.3 Plot of Residuals Versus Fitted Values _{ij} = 100
    4-1.4 Selecting a Variance-Stabilizing Transformation = 103
    4-1.5 Plots of Residuals Versus Other Variables = 108
    4-1.6 Discovering Dispersion Effects = 109
  4-2 Choice of Sample Size = 110
    4-2.1 Operating Characteristic Curves = 110
    4-2.2 Specifying a Standard Deviation Increase = 114
    4-2.3 Confidence Interval Estimation Method = 115
  4-3 Fitting Response Curves in the Single-Factor One-Way Model = 116
    4-3.1 General Regression Approach = 116
    4-3.2 Orthogonal Polynomials = 118
  4-4 The Regression Approach to the Analysis of Variance = 121
  4-5 Nonparametric Methods in the Analysis of Variance = 126
    4-5.1 The Kruskal-Wallis Test = 126
    4-5.2 General Comments on the Rank Transformation = 127
  4-6 Repeated Measures = 128
  4-7 Problems = 130
Chapter 5. Randomized Blocks, Latin Squares, and Related Designs = 134
  5-1 The Randomized Complete Block Design = 134
    5-1.1 Statistical Analysis = 135
    5-1.2 Model Adequacy Checking = 146
    5-1.3 Estimating Missing Values = 148
    5-1.4 Estimating Model Parameters and the General Regression Significance Test = 151
    5-1.5 Sample Computer Output = 154
  5-2 The Latin Square Design = 156
  5-3 The Graeco-Latin Square Design = 166
  5-4 Problems = 169
Chapter 6. Incomplete Block Designs = 176
  6-1 Introduction = 176
  6-2 Balanced Incomplete Block Designs = 176
    6-2.1 Statistical Analysis = 177
    6-2.2 Least Squares Estimation of the Parameters = 183
  6-3 Recovery of Interblock Information in the Balanced Incomplete Block Design = 184
  6-4 Partially Balanced Incmplete Block Designs = 187
  6-5 Youden Squares = 190
  6-6 Lattice Designs = 193
  6-7 Problems = 194
Chapter 7. Introduction to Factorial Designs = 197
  7-1 Basic Definitions and Principles = 197
  7-2 The Advantage of Factorials = 199
  7-3 The Two-Factor Factorial Design = 201
    7-3.1 An Example = 201
    7-3.2 Statistical Analysis of the Fixed Effects Model = 203
    7-3.3 Model Adequacy Checking = 210
    7-3.4 Estimating the Model Parameters = 213
    7-3.5 Choice of Sample Size = 216
    7-3.6 The Assumption of No Interaction in a Two-Factor Model = 217
    7-3.7 One Observation per Cell = 218
  7-4 Random and Mixed Models = 222
    7-4.1 The Random Effects Model = 222
    7-4.2 Mixed Models = 224
    7-4.3 Choice of Sample Size = 228
  7-5 The General Factorial Design = 228
  7-6 Fitting Response Curves and Surfaces = 237
  7-7 Dealing with Unbalanced Data = 244
    7-7.1 Proportional Data : an Easy Case = 245
    7-7.2 Approximate Methods = 247
    7-7.3 The Exact method = 249
Chapter 8. Rules for Sums of Squares and Expected Mean Squares = 257
  8-1 Rules for Sums of Squares = 257
  8-2 Rules for Expected Mean Squeares = 259
  8-3 Approximate F Tests = 262
  8-4 Problems = 268
Chapter 9. The 2k Factorial Design = 270
  9-1 Intorduction = 270
  9-2 The 2² Design = 270
  9-3 The 2³ Design = 278
  9-4 The General 2k Design = 288
  9-5 A Stingle Replicate of the 2^k Design = 289
  9-6 The Addition of Center Points to the 2^k Design = 304
  9-7 Yates' Algorithm for the 2^k Design = 309
  9-8 Problems = 310
Chapter 10. Confounding in the 2^k Factorial = 319
  10-1 Introduction = 319
  10-2 The 2k Factorial Design in Two Blocks = 319
  10-3 The 2k Factorial Design in Four Blocks = 326
  10-4 The 2k Factorial Design in in 2^p Blocks = 329
  10-5 Partial Confounding = 329
  10-6 Problems = 333
Chapter 11. Two-Level Fractional Factorial Designs = 335
  11-1 Intorduction = 335
  11-2 The One-Half Fraction of the 2^k Design = 336
  11-3 The One-Quarter Fraction of the 2^k Design = 349
  11-4 The General 2k-p Fractional factorial Design = 358
  11-5 Resolution Ⅲ Designs = 367
  11-6 Resolution Ⅳ and Ⅴ Designs = 375
  11-7 Summary = 378
  11-8 Problems = 378
Chapter 12. Some Other Topics Regarding Factorial and Fractional Factorial Designs = 387
  12-1 The 3^k Factorial Design = 387
    12-1.1 Notation and Motivation for the 3^k Design = 387
    12-1.2 The 3^2 Design = 388
    12-1.3 The 3^3 Design = 391
    12-1.4 The General 3k Design = 395
    12-1.5 Yates' Algorithm for the 2k Design = 397
  12-2 Confounding in the 2k Factorial Design = 399
    12-2.1 The 3k factorial Design in Three Blocks = 399
    12-2.2 The 3k factorial Design in Nine Blocks = 402
    12-2.3 The 3k factorial Design in 3p Blocks = 404
  12-3 Factional Replication of the 3k Factorial Design = 405
    12-3.1 The One-Third Faction of the 3k Design = 405
    12-3.2 Other 3k-p Fractional Factorial Design = 408
  12-4 Factorials with Mixed Levels = 410
    12-4.1 Factors at Two and Three Levels = 410
    12-4.2 Factors at Two and Four Levels = 412
  12-5 Taguchi's contributions to Experimental Design and Quality Engineering = 414
    12-5.1 The Taguchi Philogophy = 415
    12-5.2 The Taguchi Approach to Parameter Desgin = 417
  12-6 Problems = 433
Chapter 13. Nested or Hierarchial Designs = 439
  13-1 Intorduction = 439
  13-2 The Two-Stage Nested Design = 440
    13-2.1 Statistical Analysis = 440
    13-2.2 Diagnostic Checking = 445
    13-2.3 Estimation of the Model Parameters = 446
  13-3 The General m-Stage Nested Design = 450
  13-4 Designs with Nested and Crossed Factors = 452
  13-5 Problems = 456
Chapter 14. Multifactor Experiments with Randomization Restrictions = 461
  14-1 Randomized Blocks and latin Squares as Multifactor Designs = 461
  14-2 The Split-Plot Design = 468
  14-3 The Split-Split-Plot Design = 472
  14-4 Problems = 475
Chapter 15. Regression Analysis = 479
  15-1 Introduction = 479
  15-2 Simple Linear Regression = 479
  15-3 Hypothesis Testing in Simple Linear Regression = 486
  15-4 Interval Estimation in Simple Linear Regression = 489
  15-5 Model Adequacy Checking = 493
    15-5.1 Residual Analysis = 493
    15-5.2 The Lack-of-Fit Test = 493
    15-5.3 The Coefficient of Determination = 497
  15-6 Multiple Linear Regression = 498
  15-7 Hypothesis Testing in Multiple Linear Regression = 507
  15-8 Other Linear Regression Models = 512
  15-9 Sample Computer Printout = 515
  15-10 Problems = 515
Chapter 16. Response Surface Methods and Designs = 521
  16-1 Introduction to Response Surface Methodology = 521
  16-2 The Method of Steepest Ascent = 523
  16-3 Analysis of a Second-Order Model = 531
    16-3.1 Location of the Stationary Point = 531
    16-3.2 Characterizing the Response Surface = 532
    16-3.3 Ridge Systems = 538
  16-4 Experimental Designs for Ftting Response Surfaces = 541
    16-4.1 Designs for Fitting the First-Order Model =541
    16-4.2 Designs for Fitting the Second-Order Model =542
    16-4.3 Blocking in Response Surfce Designs = 548
  16-5 Mixture Experiments = 551
  16-6 Evolutionary Operation = 558
  16-7 Problems = 563
Chapter 17. Analysis of Covariance = 569
  17-1 Introduction = 569
  17-2 A Single-Factor Design with One Covariate = 569
  17-3 Development by the General Regression Significance Test = 581
  17-4 Other Covariance Models = 584
  17-5 Problems = 587
Bibliography = 590
Appendix = 597
  Table Ⅰ Cumulative Standard Normal Distribution = 598
  Table Ⅱ Percentage Points of the t Distribution = 600
  Table Ⅲ Percentage Points of the χ2 Distribution = 601
  Table Ⅳ Percentage Points of the F Distributio = 602
  Table Ⅴ Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance = 607
  Table Ⅵ Operating Characteristic Curves for the Random Effects Model Analysis of Variance = 611
  Table Ⅶ Significant Ranges for Duncan's Multiple Range Test = 615
  Table Ⅷ Percentage Points of the Studentized Range Statistic = 617
  Table Ⅸ Critical Values for Dunnett's Test for Comparing Treatments with a Control = 619
  Table Ⅹ Coefficients of Orthogonal Polynomials = 623
  Table xi Random Numbers = 624
  Table xii Alias Relationships for 2k-p Factorial Designs with k≤11 and n≤64 = 626
Index = 645