Design and analysis of experiments

자료유형	단행본
서명/저자사항	Design and analysis of experiments / Douglas C. Montgomery.
개인저자	Montgomery, Douglas C.
판사항	3rd ed.
발행사항	New York : Wiley, c1991.
형태사항	xvii, 649 p. : ill. ; 25 cm.
ISBN	0471520004 047152994X
서지주기	Includes bibliographical references and index.
일반주제명	Experimental design
언어	영어

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

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