Design and analysis of experiments

목차 (Table of Contents)

• 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 $$\sigma _1^2\ne \sigma _2^2$$ = 34
• 2-4.5 The Case Where $$\sigma _1^2$$ and $$\sigma _2^2$$ 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$$\acute e$$'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 $$2^k$$ Factorial Design = 270
• 9-1 Intorduction = 270
• 9-2 The 2² Design = 270
• 9-3 The 2³ Design = 278
• 9-4 The General $$2^k$$ 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 $$2^k$$ Factorial Design in Two Blocks = 319
• 10-3 The $$2^k$$ Factorial Design in Four Blocks = 326
• 10-4 The $$2^k$$ 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 $$2^{k-p}$$ 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 $$3^k$$ Design = 395
• 12-1.5 Yates' Algorithm for the $$2^k$$ Design = 397
• 12-2 Confounding in the $$2^k$$ Factorial Design = 399
• 12-2.1 The $$3^k$$ factorial Design in Three Blocks = 399
• 12-2.2 The $$3^k$$ factorial Design in Nine Blocks = 402
• 12-2.3 The $$3^k$$ factorial Design in $$3^p$$ Blocks = 404
• 12-3 Factional Replication of the $$3^k$$ Factorial Design = 405
• 12-3.1 The One-Third Faction of the $$3^k$$ Design = 405
• 12-3.2 Other $$3^{k-p}$$ 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 $$\chi ^2$$ 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 $$2^{k-p}$$ Factorial Designs with $$k\le 11$$ and $$n\le 64$$ = 626
• Index = 645