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Viser: Design and Analysis of Experiments
Design and Analysis of Experiments
Douglas C. Montgomery
(2012)
Sprog: Engelsk
John Wiley & Sons, Limited
648,00 kr.
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Detaljer om varen
- 8. Udgave
- Paperback: 752 sider
- Udgiver: John Wiley & Sons, Limited (Juni 2012)
- ISBN: 9781118097939
The eighth edition of this best selling text continues to help senior under graduate students in engineering, business, and statistics-as well as working practitioners-to design and analyse experiments for improving the quality, efficiency and performance of working systems.
The eighth edition of Design and Analysis of Experiments maintains its comprehensive coverage by including: new examples, exercises, and problems (including in the areas of biochemistry and biotechnology); new topics and problems in the area of response surface; new topics in nested and split-plot design; and the residual maximum likelihood method is now emphasized throughout the book.
Continuing to place a strong focus on the use of the computer, this edition includes software examples taken from the four most dominant programs in the field: Design-Expert, Minitab, JMP, and SAS.
Preface v 1 Introduction 1
1.1 Strategy of Experimentation 1
1.2 Some Typical Applications of Experimental Design 8
1.3 Basic Principles 11
1.4 Guidelines for Designing Experiments 14
1.5 A Brief History of Statistical Design 21
1.6 Summary: Using Statistical Techniques in Experimentation 22
1.7 Problems 23 2 Simple Comparative Experiments 25
2.1 Introduction 25
2.2 Basic Statistical Concepts 27
2.3 Sampling and Sampling Distributions 30
2.4 Inferences About the Differences in Means, Randomized Designs 36
2.4.1 Hypothesis Testing 36
2.4.2 Confidence Intervals 43
2.4.3 Choice of Sample Size 44
2.4.4 The Case Where Ï?²1 â? Ï?²2 48
2.4.5 The Case Where Ï?²1 and Ï?²2 are Known 50
2.4.6 Comparing a Single Mean to a Specified Value 50
2.4.7 Summary 51
2.5 Inferences About the Differences in Means, Paired Comparison Designs 53
2.5.1 The Paired Comparison Problem 53
2.5.2 Advantages of the Paired Comparison Design 56
2.6 Inferences About the Variances of Normal Distributions 57
2.7 Problems 59 3 Experiments with a Single Factor: The Analysis of Variance 65
3.1 An Example 66
3.2 The Analysis of Variance 68
3.3 Analysis of the Fixed Effects Model 70
3.3.1 Decomposition of the Total Sum of Squares 71
3.3.2 Statistical Analysis 73
3.3.3 Estimation of the Model Parameters 78
3.3.4 Unbalanced Data 79
3.4 Model Adequacy Checking 80
3.4.1 The Normality Assumption 80
3.4.2 Plot of Residuals in Time Sequence 82
3.4.3 Plot of Residuals Versus Fitted Values 83
3.4.4 Plots of Residuals Versus Other Variables 88
3.5 Practical Interpretation of Results 89
3.5.1 A Regression Model 89
3.5.2 Comparisons Among Treatment Means 90
3.5.3 Graphical Comparisons of Means 91
3.5.4 Contrasts 92
3.5.5 Orthogonal Contrasts 94
3.5.6 Scheffé''s Method for Comparing All Contrasts 96
3.5.7 Comparing Pairs of Treatment Means 97
3.5.8 Comparing Treatment Means with a Control 101
3.6 Sample Computer Output 102
3.7 Determining Sample Size 105
3.7.1 Operating Characteristic Curves 105
3.7.2 Specifying a Standard Deviation Increase 108
3.7.3 Confidence Interval Estimation Method 109
3.8 Other Examples of Single-Factor Experiments 110
3.8.1 Chocolate and Cardiovascular Health 110
3.8.2 A Real Economy Application of a Designed Experiment 110
3.8.3 Discovering Dispersion Effects 114
3.9 The Random Effects Model 116
3.9.1 A Single Random Factor 116
3.9.2 Analysis of Variance for the Random Model 117
3.9.3 Estimating the Model Parameters 118
3.10 The Regression Approach to the Analysis of Variance 125
3.10.1 Least Squares Estimation of the Model Parameters 125
3.10.2 The General Regression Significance Test 126
3.11 Nonparametric Methods in the Analysis of Variance 128
3.11.1 The Kruskal-Wallis Test 128
3.11.2 General Comments on the Rank Transformation 130
3.12 Problems 130 4 Randomized Blocks, Latin Squares, and Related Designs 139
4.1 The Randomized Complete Block Design 139
4.1.1 Statistical Analysis of the RCBD 141
4.1.2 Model Adequacy Checking 149
4.1.3 Some Other Aspects of the Randomized Complete Block Design 150
4.1.4 Estimating Model Parameters and the General Regression Significance Test 155
4.2 The Latin Square Design 158
4.3 The Graeco-Latin Square Design 165
4.4 Balanced Incomplete Block Designs 168
4.4.1 Statistical Analysis of the BIBD 168
4.4.2 Least Squares Estimation of the Parameters 172
4.4.3 Recovery of Interblock Information in the BIBD 174
4.5 Problems 177 5 Introduction to Factorial Designs 183
5.1 Basic Definitions and Principles 183
5.2 The Advantage of Factorials 186
5.3 The Two-Factor Factorial Design 187
5.3.1 An Example 187
5.3.2 Statistical Analysis of the Fixed Effects Model 189
5.3.3 Model Adequacy Checking 198
5.3.4 Estimating the Model Parameters 198
5.3.5 Choice of Sample Size 201
5.3.6 The Assumption of No Interaction in a Two-Factor Model 202
5.3.7 One Observation per Cell 203
5.4 The General Factorial Design 206
5.5 Fitting Response Curves and Surfaces 211
5.6 Blocking in a Factorial Design 219
5.7 Problems 225 6 The 2 k Factorial Design 233
6.1 Introduction 233
6.2 The 22 Design 234
6.3 The 23 Design 241
6.4 The General 2 k Design 253
6.5 A Single Replicate of the 2 k Design 255
6.6 Additional Examples of Unreplicated 2 k Design 268
6.7 2 k Designs are Optimal Designs 280
6.8 The Addition of Center Points to the 2 k Design 285
6.9 Why We Work with Coded Design Variables 290
6.10 Problems 292 7 Blocking and Confounding in the 2 k Factorial Design 304
7.1 Introduction 304
7.2 Blocking a Replicated 2 k Factorial Design 305
7.3 Confounding in the 2 k Factorial Design 306
7.4 Confounding the 2 k Factorial Design in Two Blocks 306
7.5 Another Illustration of Why Blocking is Important 312
7.6 Confounding the 2 k Factorial Design in Four Blocks 313
7.7 Confounding the 2 k Factorial Design in 2 p Blocks 315
7.8 Partial Confounding 316
7.9 Problems 319 8 Two-Level Fractional Factorial Designs 320
8.1 Introduction 320
8.2 The One-Half Fraction of the 2 k Design 321
8.2.1 Definitions and Basic Principles 321
8.2.2 Design Resolution 323
8.2.3 Construction and Analysis of the One-Half Fraction 324
8.3 The One-Quarter Fraction of the 2 k Design 333
8.4 The General 2 k- p Fractional Factorial Design 340
8.4.1 Choosing a Design 340
8.4.2 Analysis of 2 k- p Fractional Factorials 343
8.4.3 Blocking Fractional Factorials 344
8.5 Alias Structures in Fractional Factorials and other Designs 349
8.6 Resolution III Designs 351
8.6.1 Constructing Resolution III Designs 351
8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 353
8.6.3 Plackett-Burman Designs 357
8.7 Resolution IV and V Designs 366
8.7.1 Resolution IV Designs 366
8.7.2 Sequential Experimentation with Resolution IV Designs 367
8.7.3 Resolution V Designs 373
8.8 Supersaturated Designs 374
8.9 Summary 375
8.10 Problems 376 9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 394
9.1 The 3 k Factorial Design 395
9.1.1 Notation and Motivation for the 3 k Design 395
9.1.2 The 32 Design 396
9.1.3 The 33 Design 397
9.1.4 The General 3 k Design 402
9.2 Confounding in the 3 k Factorial Design 402
9.2.1 The 3 k Factorial Design in Three Blocks 403
9.2.2 The 3 k Factorial Design in Nine Blocks 406
9.2.3 The 3 k Factorial Design in 3 p Blocks 407
9.3 Fractional Replication of the 3 k Factorial Design 408
9.3.1 The One-Third Fraction of the 3 k Factorial Design 408
9.3.2 Other 3 k- p Fractional Factorial Designs 410
9.4 Factorials with Mixed Levels 412
9.4.1 Factors at Two and Three Levels 412
9.4.2 Factors at Two and Four Levels 414
9.5 Nonregular Fractional Factorial Designs 415
9.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs 418
9.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs 425
9.5.3 Analysis of Nonregular Fractional Factorial Designs 427
9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 431
9.6.1 Design Optimality Criteria 433
9.6.2 Examples of Optimal Designs 433
9.6.3 Extensions of the Optimal Design Approach 443
9.7 Problems 444 10 Fitting Regression Models 449
10.1 Introduction 449
10.2 Linear Regression Models 450
10.3 Estimation of the Parameters in Linear Regression Models 451
10.4 Hypothesis Testing in Multiple Regression 462
10.4.1 Test for Significance of Regression 462
10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients 464
10.5 Confidence Intervals in Multiple Regression 467
10.5.1 Confidence Intervals on the Individual Regression Coefficients 467
10.5.2 Confidence Interval on the Mean Response 468
10.6 Prediction of New Response Observations 468
10.7 Regression Model Diagnostics 470
10.7.1 Scaled Residuals and PRESS 470
10.7.2 Influence Diagnostics 472
10.8 Testing for Lack of Fit 473
10.9 Problems 475 11 Response Surface Methods and Designs 478
11.1 Introduction to Response Surface Methodology 478
11.2 The Method of Steepest Ascent 480
11.3 Analysis of a Second-Order Response Surface 486
11.3.1 Location of the Stationary Point 486
11.3.2 Characterizing the Response Surface 488
11.3.3 Ridge Systems 495
11.3.4 Multiple Responses 496
11.4 Experimental Designs for Fitting Response Surfaces 500
11.4.1 Designs for Fitting the First-Order Model 501
11.4.2 Designs for Fitting the Second-Order Model 501
11.4.3 Blocking in Response Surface Designs 507
11.4.4 Optimal D
1.1 Strategy of Experimentation 1
1.2 Some Typical Applications of Experimental Design 8
1.3 Basic Principles 11
1.4 Guidelines for Designing Experiments 14
1.5 A Brief History of Statistical Design 21
1.6 Summary: Using Statistical Techniques in Experimentation 22
1.7 Problems 23 2 Simple Comparative Experiments 25
2.1 Introduction 25
2.2 Basic Statistical Concepts 27
2.3 Sampling and Sampling Distributions 30
2.4 Inferences About the Differences in Means, Randomized Designs 36
2.4.1 Hypothesis Testing 36
2.4.2 Confidence Intervals 43
2.4.3 Choice of Sample Size 44
2.4.4 The Case Where Ï?²1 â? Ï?²2 48
2.4.5 The Case Where Ï?²1 and Ï?²2 are Known 50
2.4.6 Comparing a Single Mean to a Specified Value 50
2.4.7 Summary 51
2.5 Inferences About the Differences in Means, Paired Comparison Designs 53
2.5.1 The Paired Comparison Problem 53
2.5.2 Advantages of the Paired Comparison Design 56
2.6 Inferences About the Variances of Normal Distributions 57
2.7 Problems 59 3 Experiments with a Single Factor: The Analysis of Variance 65
3.1 An Example 66
3.2 The Analysis of Variance 68
3.3 Analysis of the Fixed Effects Model 70
3.3.1 Decomposition of the Total Sum of Squares 71
3.3.2 Statistical Analysis 73
3.3.3 Estimation of the Model Parameters 78
3.3.4 Unbalanced Data 79
3.4 Model Adequacy Checking 80
3.4.1 The Normality Assumption 80
3.4.2 Plot of Residuals in Time Sequence 82
3.4.3 Plot of Residuals Versus Fitted Values 83
3.4.4 Plots of Residuals Versus Other Variables 88
3.5 Practical Interpretation of Results 89
3.5.1 A Regression Model 89
3.5.2 Comparisons Among Treatment Means 90
3.5.3 Graphical Comparisons of Means 91
3.5.4 Contrasts 92
3.5.5 Orthogonal Contrasts 94
3.5.6 Scheffé''s Method for Comparing All Contrasts 96
3.5.7 Comparing Pairs of Treatment Means 97
3.5.8 Comparing Treatment Means with a Control 101
3.6 Sample Computer Output 102
3.7 Determining Sample Size 105
3.7.1 Operating Characteristic Curves 105
3.7.2 Specifying a Standard Deviation Increase 108
3.7.3 Confidence Interval Estimation Method 109
3.8 Other Examples of Single-Factor Experiments 110
3.8.1 Chocolate and Cardiovascular Health 110
3.8.2 A Real Economy Application of a Designed Experiment 110
3.8.3 Discovering Dispersion Effects 114
3.9 The Random Effects Model 116
3.9.1 A Single Random Factor 116
3.9.2 Analysis of Variance for the Random Model 117
3.9.3 Estimating the Model Parameters 118
3.10 The Regression Approach to the Analysis of Variance 125
3.10.1 Least Squares Estimation of the Model Parameters 125
3.10.2 The General Regression Significance Test 126
3.11 Nonparametric Methods in the Analysis of Variance 128
3.11.1 The Kruskal-Wallis Test 128
3.11.2 General Comments on the Rank Transformation 130
3.12 Problems 130 4 Randomized Blocks, Latin Squares, and Related Designs 139
4.1 The Randomized Complete Block Design 139
4.1.1 Statistical Analysis of the RCBD 141
4.1.2 Model Adequacy Checking 149
4.1.3 Some Other Aspects of the Randomized Complete Block Design 150
4.1.4 Estimating Model Parameters and the General Regression Significance Test 155
4.2 The Latin Square Design 158
4.3 The Graeco-Latin Square Design 165
4.4 Balanced Incomplete Block Designs 168
4.4.1 Statistical Analysis of the BIBD 168
4.4.2 Least Squares Estimation of the Parameters 172
4.4.3 Recovery of Interblock Information in the BIBD 174
4.5 Problems 177 5 Introduction to Factorial Designs 183
5.1 Basic Definitions and Principles 183
5.2 The Advantage of Factorials 186
5.3 The Two-Factor Factorial Design 187
5.3.1 An Example 187
5.3.2 Statistical Analysis of the Fixed Effects Model 189
5.3.3 Model Adequacy Checking 198
5.3.4 Estimating the Model Parameters 198
5.3.5 Choice of Sample Size 201
5.3.6 The Assumption of No Interaction in a Two-Factor Model 202
5.3.7 One Observation per Cell 203
5.4 The General Factorial Design 206
5.5 Fitting Response Curves and Surfaces 211
5.6 Blocking in a Factorial Design 219
5.7 Problems 225 6 The 2 k Factorial Design 233
6.1 Introduction 233
6.2 The 22 Design 234
6.3 The 23 Design 241
6.4 The General 2 k Design 253
6.5 A Single Replicate of the 2 k Design 255
6.6 Additional Examples of Unreplicated 2 k Design 268
6.7 2 k Designs are Optimal Designs 280
6.8 The Addition of Center Points to the 2 k Design 285
6.9 Why We Work with Coded Design Variables 290
6.10 Problems 292 7 Blocking and Confounding in the 2 k Factorial Design 304
7.1 Introduction 304
7.2 Blocking a Replicated 2 k Factorial Design 305
7.3 Confounding in the 2 k Factorial Design 306
7.4 Confounding the 2 k Factorial Design in Two Blocks 306
7.5 Another Illustration of Why Blocking is Important 312
7.6 Confounding the 2 k Factorial Design in Four Blocks 313
7.7 Confounding the 2 k Factorial Design in 2 p Blocks 315
7.8 Partial Confounding 316
7.9 Problems 319 8 Two-Level Fractional Factorial Designs 320
8.1 Introduction 320
8.2 The One-Half Fraction of the 2 k Design 321
8.2.1 Definitions and Basic Principles 321
8.2.2 Design Resolution 323
8.2.3 Construction and Analysis of the One-Half Fraction 324
8.3 The One-Quarter Fraction of the 2 k Design 333
8.4 The General 2 k- p Fractional Factorial Design 340
8.4.1 Choosing a Design 340
8.4.2 Analysis of 2 k- p Fractional Factorials 343
8.4.3 Blocking Fractional Factorials 344
8.5 Alias Structures in Fractional Factorials and other Designs 349
8.6 Resolution III Designs 351
8.6.1 Constructing Resolution III Designs 351
8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects 353
8.6.3 Plackett-Burman Designs 357
8.7 Resolution IV and V Designs 366
8.7.1 Resolution IV Designs 366
8.7.2 Sequential Experimentation with Resolution IV Designs 367
8.7.3 Resolution V Designs 373
8.8 Supersaturated Designs 374
8.9 Summary 375
8.10 Problems 376 9 Additional Design and Analysis Topics for Factorial and Fractional Factorial Designs 394
9.1 The 3 k Factorial Design 395
9.1.1 Notation and Motivation for the 3 k Design 395
9.1.2 The 32 Design 396
9.1.3 The 33 Design 397
9.1.4 The General 3 k Design 402
9.2 Confounding in the 3 k Factorial Design 402
9.2.1 The 3 k Factorial Design in Three Blocks 403
9.2.2 The 3 k Factorial Design in Nine Blocks 406
9.2.3 The 3 k Factorial Design in 3 p Blocks 407
9.3 Fractional Replication of the 3 k Factorial Design 408
9.3.1 The One-Third Fraction of the 3 k Factorial Design 408
9.3.2 Other 3 k- p Fractional Factorial Designs 410
9.4 Factorials with Mixed Levels 412
9.4.1 Factors at Two and Three Levels 412
9.4.2 Factors at Two and Four Levels 414
9.5 Nonregular Fractional Factorial Designs 415
9.5.1 Nonregular Fractional Factorial Designs for 6, 7, and 8 Factors in 16 Runs 418
9.5.2 Nonregular Fractional Factorial Designs for 9 Through 14 Factors in 16 Runs 425
9.5.3 Analysis of Nonregular Fractional Factorial Designs 427
9.6 Constructing Factorial and Fractional Factorial Designs Using an Optimal Design Tool 431
9.6.1 Design Optimality Criteria 433
9.6.2 Examples of Optimal Designs 433
9.6.3 Extensions of the Optimal Design Approach 443
9.7 Problems 444 10 Fitting Regression Models 449
10.1 Introduction 449
10.2 Linear Regression Models 450
10.3 Estimation of the Parameters in Linear Regression Models 451
10.4 Hypothesis Testing in Multiple Regression 462
10.4.1 Test for Significance of Regression 462
10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients 464
10.5 Confidence Intervals in Multiple Regression 467
10.5.1 Confidence Intervals on the Individual Regression Coefficients 467
10.5.2 Confidence Interval on the Mean Response 468
10.6 Prediction of New Response Observations 468
10.7 Regression Model Diagnostics 470
10.7.1 Scaled Residuals and PRESS 470
10.7.2 Influence Diagnostics 472
10.8 Testing for Lack of Fit 473
10.9 Problems 475 11 Response Surface Methods and Designs 478
11.1 Introduction to Response Surface Methodology 478
11.2 The Method of Steepest Ascent 480
11.3 Analysis of a Second-Order Response Surface 486
11.3.1 Location of the Stationary Point 486
11.3.2 Characterizing the Response Surface 488
11.3.3 Ridge Systems 495
11.3.4 Multiple Responses 496
11.4 Experimental Designs for Fitting Response Surfaces 500
11.4.1 Designs for Fitting the First-Order Model 501
11.4.2 Designs for Fitting the Second-Order Model 501
11.4.3 Blocking in Response Surface Designs 507
11.4.4 Optimal D
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