Design and Analysis of Experiments by Douglas Montgomery
ContentsAbout This Book ........................................................................................ ix
About These Authors ................................................................................ xiii
Acknowledgments ..................................................................................... xv
Chapter 1 Introduction ............................................................................... 1
Chapter 2 Simple Comparative Experiments .............................................. 5
Section 2.2 Basic Statistical Concepts .................................................................................. 6
Section 2.4.1 Hypothesis Testing ......................................................................................... 10
Section 2.4.3 Choice of Sample Size ................................................................................... 12
Section 2.5.1 The Paired Comparison Problem .................................................................. 17
Section 2.5.2 Advantages of the Paired Comparison Design ........................................... 18
Chapter 3 Experiments with a Single Factor: The Analysis of Variance .... 21
Section 3.1 A One-way ANOVA Example ............................................................................ 22
Section 3.4 Model Adequacy Checking ............................................................................... 32
Section 3.8.1 Single Factor Experiment .............................................................................. 46
Section 3.8.2 Application of a Designed Experiment ......................................................... 52
Section 3.8.3 Discovering Dispersion Effects ..................................................................... 54
Chapter 4 Randomized Blocks, Latin Squares, and Related Designs ........ 61
Section 4.2 Creating a Latin Square Design in JMP .......................................................... 67
Chapter 5 Introduction to Factorial Designs ............................................. 77
Example 5.1 The Battery Design Experiment ..................................................................... 78
Example 5.2 A Two-Factor Experiment with a Single Replicate....................................... 82
Example 5.3 The Soft Drink Bottling Problem .................................................................... 84
Example 5.4 The Battery Design Experiment with a Covariate ........................................ 86
Example 5.5 A 32 Factorial Experiment with Two Replicates ............................................ 89
Example 5.6 A Factorial Design with Blocking ................................................................... 97
Chapter 6 The 2k Factorial Design .......................................................... 101
Section 6.2 The 22 design ................................................................................................... 102
Example 6.1 A 23 Design ..................................................................................................... 107
Example 6.2 A Single Replicate of the 24 Design ............................................................. 109
Example 6.3 Data Transformation in a Factorial Design ................................................. 114
Example 6.5 Duplicate Measurements on the Response ............................................... 118
Example 6.6 Credit Card Marketing .................................................................................. 125
Example 6.7 A 24 Design with Center Points .................................................................... 128
Chapter 7 Blocking and Confounding in the 2k Factorial Design ............. 131
Example 7.1 A 2k Replicated Factorial Design with Blocking ......................................... 132
Example 7.2 Blocking and Confounding in an Unreplicated Design ............................. 132
Example 7.3 A 23 Design with Partial Confounding ......................................................... 134
Chapter 8 Two-Level Fractional Factorial Designs ................................. 141
Example 8.1 A Half-Fraction of the 24 Design .................................................................. 143
Example 8.2 A 25-1 Design Used for Process Improvement ............................................ 147
Example 8.3 A 24-1 Design with the Alternate Fraction .................................................... 152
Example 8.4 A 26-2 Design ................................................................................................... 153
Example 8.5 A 27-3 Design ................................................................................................... 158
Example 8.6 A 28-3 Design in Four Blocks ......................................................................... 160
Example 8.7 A Fold-Over 27-4 Resolution III Design ......................................................... 164
Example 8.8 The Plackett-Burman Design ....................................................................... 167
Section 8.7.2 Sequential Experimentation with Resolution IV Designs ......................... 168
Chapter 9 Three-Level and Mixed-Level Factorial and Fractional Factorial
Designs ................................................................................ 173
Example 9.1 The 33 Design ................................................................................................. 174
Example 9.2 The 32 Design Confounded in 3 Blocks ....................................................... 177
Example 9.3 The Spin Coating Experiment ...................................................................... 178
Example 9.4 An Experiment with Unusual Blocking Requirements ............................... 181
Chapter 10 Fitting Regression Models .................................................... 189
Example 10.1 Multiple Linear Regression Model ............................................................. 190
Example 10.2 Regression Analysis of a 23 Factorial Design ........................................... 195
Example 10.3 A 23 Factorial Design with a Missing Observation ................................... 197
Example 10.4 Inaccurate Levels in Design Factors ......................................................... 198
Example 10.6 Tests on Individual Regression Coefficients ............................................ 198
Example 10.7 Confidence Intervals on Individual Regression Coefficients .................. 199
Chapter 11 Response Surface Methods and Designs ............................. 201
Example 11.1 The Path of Steepest Ascent ...................................................................... 202
Example 11.2 Central Composite Design.......................................................................... 204
Section 11.3.4 Multiple Responses .................................................................................... 209
Example 11.4 Space Filling Design with Gaussian Process Model ................................ 214
Example 11.5 A Three-Component Mixture ...................................................................... 218
Example 11.6 Paint Formulation ........................................................................................ 222
Chapter 12 Robust Parameter Design and Process Robustness Studies 227
Example 12.1 Two Controllable Variables and One Noise Variable ............................... 228
Example 12.2 Two Controllable Variables and Three Noise Variables .......................... 230
Chapter 13 Experiments with Random Factors ....................................... 239
Example 13.1 A Measurement Systems Capability Study ............................................... 240
Example 13.3 The Unrestricted Model .............................................................................. 242
Example 13.5 A Three-Factor Factorial Experiment with Random Factors .................. 244
Example 13.6 Approximate F Tests ................................................................................... 245
Chapter 14 Nested and Split-Plot Designs .............................................. 251
Example 14.1 The Two-Stage Nested Design ................................................................... 252
Example 14.2 A Nested-Factorial Design .......................................................................... 254
Section 14.4 The Experiment on the Tensile Strength of Paper ..................................... 256
Example 14.3 A 25-1 Split-Plot Experiment ......................................................................... 259
Chapter 15 Other Design and Analysis Topics ........................................ 263
Example 15.1 Box-Cox Transformation ............................................................................. 264
Example 15.2 The Generalized Linear Model and Logistic Regression ......................... 265
Example 15.3 Poisson Regression ..................................................................................... 267
Example 15.4 The Worsted Yarn Experiment ................................................................... 269
Section 15.2 Unbalanced Data in a Factorial Design ....................................................... 270
Example 15.5 Analysis of Covariance ................................................................................ 271
Section 15.3.4 Factorial Experiments with Covariates .................................................... 273
Index ...................................................................................................... 277
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