Design and analysis of experiments

목차 (Table of Contents)

• CONTENTS
• Chapter 1. Introduction = 1
• 1-1 Strategy of Experimentation = 1
• 1-2 Some Typical Applincations of Experimental Design = 7
• 1-3 Basic Principles = 12
• 1-4 Guidelines for Designing Experiments = 14
• 1-5 Historical Perspective = 17
• 1-6 Summary : Using Statistical Techniques in Experimentation = 18
• Chapter 2. Simple Comparative Experiments = 20
• 2-1 Introduction = 20
• 2-2 Basic Statisical Concepts = 21
• 2-3 Sampling and Sampling Distributions = 26
• 2-4 Inferences About the Differences in Means Randomized Designs = 33
• 2-4.1 Hypothesis Testing = 34
• 2-4.2 Choice of Sample Size = 41
• 2-4.3 Confidence Intervals = 43
• 2-4.4 The Case Where $$\sigma _1^2$$ ≠$$\sigma _2^2$$ = 45
• 2-4.5 The Case Where $$\sigma _1^2$$ and $$\sigma _2^2$$ Are Known = 46
• 2-4.6 Comparing a Single Mean to Specified Value = 46
• 2-4.7 Summary = 48
• 2-5 Inferences About the Differences in Means, Paired Comparison Designs = 48
• 2-5.1 The Paired Comparison Problem = 48
• 2-5.2 Advantages of the Paired Comparison Dasign = 53
• 2-6 Inferences About the Varances of Normal Distributions = 54
• 2-7 Problems = 56
• Chapter 3. Experiments with a Single Factor : The Analysis of Varance = 63
• 3-1 An Example = 63
• 3-2 The Analysis of Variance = 67
• 3-3 Analysis of the Fixes Effexts Model = 68
• 3-3.1 Decomposition of the Total Sum of Squares = 69
• 3-3.2 Statistical Analysis = 72
• 3-3.3 Estimation of the Model Paramerters = 78
• 3-3.4 Unbalanced Data = 79
• 3-4 Model Adequarcy Checking = 79
• 3-4.1 The Normality Assumpion = 80
• 3-4.2 Plot of Residuals in Time Sequence = 83
• 3-4.3 Plot of Residuals Versus Fitted Values = 84
• 3-4.4 Selecting a Variance-Stabilizing Transformation = 87
• 3-4.5 Plots of Residuals Versus Other Variables = 92
• 3-5 Practical Interpretation of Results = 93
• 3-5.1 A Regression Model = 93
• 3-5.2 Cmparisons Among Treatment Means = 95
• 3-5.3 Graphical Comparisons of Means = 95
• 3-5.4 Contrasts = 96
• 3-5.5 Orthogonal Contrasts = 98
• 3-5.6 Scheff$$e'$$'s Method for Comparing All Contrasts = 100
• 3-5.7 Comparing Pairs of Treatment Means = 101
• 3-5.8 Comparing Treatment Means with a Control = 107
• 3-6 Sample Computer Output = 108
• 3-7 The Random Effects Model = 110
• 3-8 Problems = 117
• Chapter 4. More About Single-Factor Experiments = 126
• 4-1 Choice of Sample Size = 126
• 4-1.1 Operating Characteristic Curves = 126
• 4-1.2 Specifying a Standard Deviation Increase = 130
• 4-1.3 Confidence Interval Estimation Method = 131
• 4-2 Discovering Dispersion Effects = 132
• 4-3 Fitting Response Curves in the Single-Factor Model = 134
• 4-4 The Regression Approach to the Analysis of Variance = 137
• 4-4.1 Least Squares Extimation of the Model Parameters = 137
• 4-4.2 The General Regression Significance Test = 138
• 4-5 Nonparametric Methods in the Analysis of Variance = 143
• 4-5.1 The Kruskal-Wallis Test = 143
• 4-5.2 General Comments on the Rank Transforamtion = 145
• 4-6 Repearted Measures = 146
• 4-7 The Analysis of Covariance = 149
• 4-7.1 Description of the Procedure = 150
• 4-7.2 Computer Solution = 161
• 4-7.3 Development by the General Regression Signifiance Test = 164
• 4-8 Problems = 166
• Chapter 5. Randomized Blocks, Latin Squares, and Related Designs = 171
• 5-1 The Randomized Complete Block Design = 171
• 5-1.1 Statisical Analysis = 173
• 5-1.2 Adequarcy Checking = 182
• 5-1.3 Some Other Aspects of the Randomizes Complete Block Design = 185
• 5-1.4 Estimating Model Parameters and the General Regression Significance Test = 191
• 5-2 The Latin Square Design = 194
• 5-3 The Graeco-Latin Square Design = 205
• 5-4 Balanced Incomplete Block Designs = 208
• 5-4.1 Statistical Analysis = 208
• 5-4.2 Least Squares Estimation of the Parametrs = 216
• 5-4.3 Recovery of Interblock Information in the Balanced Incomplete Block Design = 217
• 5-5 Problem
• Chapter 6. Introduction to Factorial Designs = 228
• 6-1 Basic Definitions and Principles = 228
• 6-2 The Advantage of Factorials = 233
• 6-3 The Two-Factor Factorial Design= 234
• 6-3.1 An Example = 234
• 6-3.2 Statistical Analysis of the Fixed Effects Model = 237
• 6-3.3 Model Adequacy Checking = 243
• 6-3.4 Estimating the Model Parameters = 245
• 6-3.5 Choice of Sample Size = 249
• 6-3.6 The Assumption of No Interaction in a Two-Factor Model = 251
• 6-3.7 One Observation per Cell = 252
• 6-4 The General Factorial Design = 255
• 6-5 Fitting Response Curves and Surfaces = 263
• 6-6 Blocking in a Factorial Design = 271
• 6-7 Unbalanced Data in a Factorial Design = 276
• 6-7.1 Proportional Data : An Easy Case = 277
• 6-7.2 Approxmate Methods = 279
• 6-7.3 The Exact Methods = 281
• 6-8 Problems = 281
• Chapter 7. The $$\mathop 2^k$$ Factorial Design = 290
• 7-1 Introduction = 290
• 7-2 The 2² Design = 291
• 7-3 The 2³ Design = 301
• 7-4 The General $$\mathop 2^k$$ Design = 315
• 7-5 ASingle REplicate of the $$\mathop 2^k$$ Design = 318
• 7-6 The addition of Center Points to the $$\mathop 2^k$$ Design = 336
• 7-7 Yates' Algorithm for the $$\mathop 2^k$$ Design = 340
• 7-8 Problems = 341
• Chapter 8. Blocking and Confounding in the $$\mathop 2^k$$ Factorial Design = 354
• 8-1 Introduction = 354
• 8-2 Blocking a Replicated $$\mathop 2^k$$ Factorial Design = 354
• 8-3 Confounding in the $$\mathop 2^k$$ Factorial Design = 356
• 8-4 Confounding in the $$\mathop 2^k$$ Factorial Design in Two Blocks = 356
• 8-5 Confounding in the $$\mathop 2^k$$ Factorial Design in four Blocks = 363
• 8-6 Confounding in the $$\mathop 2^k$$ Factorial Design in $$\mathop 2^p$$ Blocks = 365
• 8-7 Partial Confounding = 367
• 8-8 Problems = 370
• Chapter 9. Two-Level Factional Factorial Design = 372
• 9-1 Introduction = 372
• 9-2 The One-Half Fraction of the $$\mathop 2^k$$ Design = 373
• 9-3 The One-Quarter Faction of the $$\mathop 2^k$$ Design = 389
• 9-4 The General $$\mathop 2^k-p$$ Fractional Factorial Design = 398
• 9-5 Resolution Ⅲ Designs = 409
• 9-6 Resolution Ⅳ and Ⅴ Designs = 420
• 9-7 Summary = 421
• 9-8 Problems = 422
• Chapter 10. Three-Level and Mixed-Level Factorial and Fractional Factorial Designs = 436
• 10-1 the $$\mathop 3^k$$ Factorial Design = 436
• 10-1.1 Nortation and Motivation for the $$\mathop 3^k$$ Design = 436
• 10-1.2 The 3² Design = 438
• 10-1.3 The 3³ Design = 441
• 10-1.4 The General $$\mathop 3^k$$ Design = 447
• 10-1.5 Yates' Algorithm for the $$\mathop 3^k$$ Design = 448
• 10-2 Confounding in the $$\mathop 3^k$$ Factorial Design = 449
• 10-2.1 The $$\mathop 3^k$$ Factorial Design in Three Blocks = 449
• 10-2.2 The $$\mathop 3^k$$ Factorial Design in Nine Blocks = 454
• 10-2.3 The $$\mathop 3^k$$ Factorial Design in $$\mathop 3^p$$ Blocks = 455
• 10-3 Fractional Replication of the $$\mathop 3^k$$ Factorial Designs = 456
• 10-3.1 The One-Third Fraction of the 3^k Factorial Design = 456
• 10-3.2 Other $$\mathop 3^k-p$$ Fractional Factorial Designs = 460
• 10-4 Factorials with Mixed Levels = 461
• 10-4.1 Factors at Two and Three Levels = 462
• 10-4.2 Factors at Two and Four Levels = 464
• 10-5 Problems = 466
• Chapter 11. Factorial Experiments with Random Factors = 470
• 11-1 The Rwo Factor Factorial with Random Factors = 471
• 11-2 The Rwo Factor Mixed Model = 475
• 11-3 Use of Operating Characteristic Curver in Models with Random Factors = 480
• 11-4 for Expected Mean Squares = 480
• 11-5 Approximate F Tests = 486
• 11-6 Some Additional Topics on Estimation of Variance Cmponents = 491
• 11-6.1 Approximate Confidence Intervalson Variance Components = 491
• 11-6.2 The Modified Large-Sample Method = 494
• 11-6.3 Maximum Likelihood Estimation of Variance Components = 496
• 11-7 problems = 502
• Chapter 12. Nerted and Split-Plot Designs = 506
• 12-1 The Two-Stage Nested Design = 506
• 12-1.1 Statistical Analysis = 507
• 12-1.2 Dianostic Checking = 512
• 12-1.3 Variance Components = 514
• 12-1.4 Staggered Nested Designs = 515
• 12-2 The General m-Stage Nested Design = 516
• 12-3 Designs with Both Nested and Factorial Factors = 519
• 12-4 The Split-Plot Design = 521
• 12-5 The Split-Split-Plot Design = 526
• 12-6 Problems = 529
• Chapter 13. Fitting Regression Models = 536
• 13-1 Introduction = 536
• 13-2 Liner Regression Models = 537
• 13-3 Estimation of the Parameters in Linear Regression Models = 538
• 13-4 Hypothesis Testing in Multiple Regression = 554
• 13-4.1 Test for Significance of Regression = 555
• 13-4.2 Tests on Individual Regression Coefficients and Groups of Coefficients = 557
• 13-5 Confidence Intervals in Multiple Regression = 561
• 13-5.1 Confidence Intervals on the Individual Reression Coefficients = 561
• 13-5.2 Confidence Interval on the Mean Response = 562
• 13-6 Preduiction of new Response Observations = 562
• 13-7 Regression Model Diagnostics = 563
• 13-7.1 Scaled Residuals and PRESS = 563
• 13-7.2 Influence Diagnostics = 563
• 13-8 Testing for Lake of Fit = 566
• 13-9 Problems = 569
• Chapter 14. Response Surface Methods and Other Approaches to Process Optimization = 575
• 14-1 Introduction to Response Surface Methodology = 575
• 14-2 The Method of Steepest Ascent = 578
• 14-3 Analysis of a Second-Order Response Surface = 585
• 14-3.1 Location of the the Stationary Point = 585
• 14-3.2 Characterizing the Response Surface = 587
• 14-3.3 Ridge Systems = 595
• 14-3.4 Multiple Responses = 596
• 14-4 Expermental Designs for Fitting Response Surfaces = 599
• 14-4.1 Design for Fitting the First-Order Model = 600
• 14-4.2 Designs for Fitting the Second-Order Model = 601
• 14-4.3 Blocking in Response Surface Desings = 606
• 14-5 Mixture Experiments = 611
• 14-6 Evolutionary Operation = 616
• 14-7 Taguchi's Contributions to Experimental Design and Quality Engineering = 622
• 14-7.1 The Taguchi Philosophy = 623
• 14-7.2 The Taguchi Approach to Parameter Design = 625
• 14-8 Problems = 642
• Bibliography = 652
• Appendix = 656
• Table Ⅰ. Cumulative Standard Normal Distribution = 657
• Table Ⅱ. Percentage Points of the t Distribution = 659
• Table Ⅲ. Percentage Points of the X²Distribution = 660
• Table Ⅳ. Percentage Points of the F Distribution = 661
• Table Ⅴ. Operating Characteistic Curves for the Fixed Effects Model Analysis of Variance = 666
• Table Ⅵ. PerceOperating Charctterstic Curves for the Random Effects Model Analysis of Variance = 670
• Table Ⅶ. Significant Ranges for Duncan's Multiple Range Test = 674
• Table Ⅷ. Percentage Points of Studentized Range Statistic = 675
• Table Ⅸ. Critical Values for Dunnett' s Test for Comparing Treatments with a Control = 677
• Table Ⅹ. Coefficients of Orthogonal Polynomials = 680
• Table XI. Random Numbers = 681
• Table XII. Alias Relationships for $$\mathop 2^k-p$$ Fractional Factorial Designs with k≤15 and n≤64 = 682
• Index = 699