Statistical Design and Analysis of Experiments – With Applications to Engineering and Science

Statistical Design and Analysis of Experiments – With Applications to Engineering and Science
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Robert L. Mason, Richard F. Gunst, James L. Hess
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9 نوفمبر 2021
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Statistical Design and Analysis of Experiments
With Applications to Engineering and Science
Second Edition
Robert L. Mason
Southwest Research Institute
San Antonio, Texas
Richard F. Gunst
Department of Statistical Science
Southern Methodist University
Dallas, Texas
James L. Hess
Leggett and Platt. Inc.
Carthage, Missouri
Contents
Preface vii
PART I FUNDAMENTAL STATISTICAL CONCEPTS 1

  1. Statistics in Engineering and Science 3
    1.1. The Role of Statistics in Experimentation, 5
    1.2. Populations and Samples, 9
    1.3. Parameters and Statistics, 19
    1.4. Mathematical and Statistical Modeling, 24
    Exercises, 28
  2. Fundamentals of Statistical Inference 33
    2.1. Traditional Summary Statistics, 33
    2.2. Statistical Inference, 39
    2.3. Probability Concepts, 42
    2.4. Interval Estimation, 48
    2.5. Statistical Tolerance Intervals, 50
    2.6. Tests of Statistical Hypotheses, 52
    2.7. Sample Size and Power, 56
    Appendix: Probability Calculations, 59
    Exercises, 64
    xixii CONTENTS
  3. Inferences on Means and Standard Deviations 69
    3.1. Inferences on a Population or Process Mean, 72
    3.1.1. Confidence Intervals, 73
    3.1.2. Hypothesis Tests, 76
    3.1.3. Choice of a Confidence Interval
    or a Test, 78
    3.1.4. Sample Size, 79
    3.2. Inferences on a Population or Process Standard
    Deviation, 81
    3.2.1. Confidence Intervals, 82
    3.2.2. Hypothesis Tests, 84
    3.3. Inferences on Two Populations or Processes Using
    Independent Pairs of Correlated Data Values, 86
    3.4. Inferences on Two Populations or Processes Using
    Data from Independent Samples, 89
    3.5. Comparing Standard Deviations from Several
    Populations, 96
    Exercises, 99
    PART II DESIGN AND ANALYSIS WITH FACTORIAL
    STRUCTURE 107
  4. Statistical Principles in Experimental Design 109
    4.1. Experimental-Design Terminology, 110
    4.2. Common Design Problems, 115
    4.2.1. Masking Factor Effects, 115
    4.2.2. Uncontrolled Factors, 117
    4.2.3. Erroneous Principles of Efficiency, 119
    4.2.4. One-Factor-at-a-Time Testing, 121
    4.3. Selecting a Statistical Design, 124
    4.3.1. Consideration of Objectives, 125
    4.3.2. Factor Effects, 126
    4.3.3. Precision and Efficiency, 127
    4.3.4. Randomization, 128
    4.4. Designing for Quality Improvement, 128
    Exercises, 132CONTENTS xiii
  5. Factorial Experiments in Completely Randomized
    Designs 140
    5.1. Factorial Experiments, 141
    5.2. Interactions, 146
    5.3. Calculation of Factor Effects, 152
    5.4. Graphical Assessment of Factor Effects, 158
    Appendix: Calculation of Effects for Factors
    with More than Two Levels, 160
    Exercises, 163
  6. Analysis of Completely Randomized Designs 170
    6.1. Balanced Multifactor Experiments, 171
    6.1.1. Fixed Factor Effects, 171
    6.1.2. Analysis-of-Variance Models, 173
    6.1.3. Analysis-of-Variance Tables, 176
    6.2. Parameter Estimation, 184
    6.2.1. Estimation of the Error Standard
    Deviation, 184
    6.2.2. Estimation of Effects Parameters, 186
    6.2.3. Quantitative Factor Levels, 189
    6.3. Statistical Tests, 194
    6.3.1. Tests on Individual Parameters, 194
    6.3.2. F-Tests for Factor Effects, 195
    6.4. Multiple Comparisons, 196
    6.4.1. Philosophy of Mean-Comparison
    Procedures, 196
    6.4.2. General Comparisons of Means, 203
    6.4.3. Comparisons Based on t-Statistics, 209
    6.4.4. Tukey’s Significant Difference
    Procedure, 212
    6.5. Graphical Comparisons, 213
    Exercises, 221
  7. Fractional Factorial Experiments 228
    7.1. Confounding of Factor Effects, 229
    7.2. Design Resolution, 237
    7.3. Two-Level Fractional Factorial Experiments, 239xiv CONTENTS
    7.3.1. Half Fractions, 239
    7.3.2. Quarter and Smaller Fractions, 243
    7.4. Three-Level Fractional Factorial Experiments, 247
    7.4.1. One-Third Fractions, 248
    7.4.2. Orthogonal Array Tables, 252
    7.5. Combined Two- and Three-Level Fractional
    Factorials, 254
    7.6. Sequential Experimentation, 255
    7.6.1. Screening Experiments, 256
    7.6.2. Designing a Sequence of Experiments, 258
    Appendix: Fractional Factorial Design Generators, 260
    Exercises, 266
  8. Analysis of Fractional Factorial Experiments 271
    8.1. A General Approach for the Analysis of Data from
    Unbalanced Experiments, 272
    8.2. Analysis of Marginal Means for Data from
    Unbalanced Designs, 276
    8.3. Analysis of Data from Two-Level, Fractional
    Factorial Experiments, 278
    8.4. Analysis of Data from Three-Level, Fractional
    Factorial Experiments, 287
    8.5. Analysis of Fractional Factorial Experiments with
    Combinations of Factors Having Two and Three
    Levels, 290
    8.6. Analysis of Screening Experiments, 293
    Exercises, 299
    PART III Design and Analysis with Random Effects 309
  9. Experiments in Randomized Block Designs 311
    9.1. Controlling Experimental Variability, 312
    9.2. Complete Block Designs, 317
    9.3. Incomplete Block Designs, 318
    9.3.1. Two-Level Factorial Experiments, 318
    9.3.2. Three-Level Factorial Experiments, 323
    9.3.3. Balanced Incomplete Block Designs, 325CONTENTS xv
    9.4. Latin-Square and Crossover Designs, 328
    9.4.1. Latin Square Designs, 328
    9.4.2. Crossover Designs, 331
    Appendix: Incomplete Block Design Generators, 332
    Exercises, 342
  10. Analysis of Designs with Random Factor Levels 347
    10.1. Random Factor Effects, 348
    10.2. Variance-Component Estimation, 350
    10.3. Analysis of Data from Block Designs, 356
    10.3.1. Complete Blocks, 356
    10.3.2. Incomplete Blocks, 357
    10.4. Latin-Square and Crossover Designs, 364
    Appendix: Determining Expected Mean Squares, 366
    Exercises, 369
  11. Nested Designs 378
    11.1. Crossed and Nested Factors, 379
    11.2. Hierarchically Nested Designs, 381
    11.3. Split-Plot Designs, 384
    11.3.1. An Illustrative Example, 384
    11.3.2. Classical Split-Plot Design
    Construction, 386
    11.4. Restricted Randomization, 391
    Exercises, 395
  12. Special Designs for Process Improvement 400
    12.1. Assessing Quality Performance, 401
    12.1.1. Gage Repeatability and Reproducibility, 401
    12.1.2. Process Capability, 404
    12.2. Statistical Designs for Process
    Improvement, 406
    12.2.1. Taguchi’s Robust Product Design
    Approach, 406
    12.2.2. An Integrated Approach, 410
    Appendix: Selected Orthogonal Arrays, 414
    Exercises, 418xvi CONTENTS
  13. Analysis of Nested Designs and Designs for Process
    Improvement 423
    13.1. Hierarchically Nested Designs, 423
    13.2. Split-Plot Designs, 428
    13.3. Gage Repeatability and Reproducibility
    Designs, 433
    13.4. Signal-to-Noise Ratios, 436
    Exercises, 440
    PART IV Design and Analysis with Quantitative
    Predictors and Factors 459
  14. Linear Regression with One Predictor Variable 461
    14.1. Uses and Misuses of Regression, 462
    14.2. A Strategy for a Comprehensive Regression
    Analysis, 470
    14.3. Scatterplot Smoothing, 473
    14.4. Least-Squares Estimation, 475
    14.4.1. Intercept and Slope Estimates, 476
    14.4.2. Interpreting Least-Squares Estimates, 478
    14.4.3. No-Intercept Models, 480
    14.4.4. Model Assumptions, 481
    14.5. Inference, 481
    14.5.1. Analysis-of-Variance Table, 481
    14.5.2. Tests and Confidence Intervals, 484
    14.5.3. No-Intercept Models, 485
    14.5.4. Intervals for Responses, 485
    Exercises, 487
  15. Linear Regression with Several Predictor Variables 496
    15.1. Least Squares Estimation, 497
    15.1.1. Coefficient Estimates, 497
    15.1.2. Interpreting Least-Squares Estimates, 499
    15.2. Inference, 503
    15.2.1. Analysis of Variance, 503
    15.2.2. Lack of Fit, 505
    15.2.3. Tests on Parameters, 508
    15.2.4. Confidence Intervals, 510CONTENTS xvii
    15.3. Interactions Among Quantitative Predictor
    Variables, 511
    15.4. Polynomial Model Fits, 514
    Appendix: Matrix Form of Least-Squares Estimators, 522
    Exercises, 525
  16. Linear Regression with Factors and Covariates
    as Predictors 535
    16.1. Recoding Categorical Predictors
    and Factors, 536
    16.1.1. Categorical Variables: Variables with Two
    Values, 536
    16.1.2. Categorical Variables: Variables with More
    Than Two Values, 539
    16.1.3. Interactions, 541
    16.2. Analysis of Covariance for Completely
    Randomized Designs, 542
    16.3. Analysis of Covariance for Randomized
    Complete Block Designs, 552
    Appendix: Calculation of Adjusted Factor Averages, 556
    Exercises, 558
  17. Designs and Analyses for Fitting Response Surfaces 568
    17.1. Uses of Response-Surface Methodology, 569
    17.2. Locating an Appropriate Experimental
    Region, 575
    17.3. Designs for Fitting Response Surfaces, 580
    17.3.1. Central Composite Design, 582
    17.3.2. Box–Behnken Design, 585
    17.3.3. Some Additional Designs, 586
    17.4. Fitting Response-Surface Models, 588
    17.4.1. Optimization, 591
    17.4.2. Optimization for Robust Parameter
    Product-Array Designs, 594
    17.4.3. Dual Response Analysis for Quality
    Improvement Designs, 597
    Appendix: Box–Behnken Design Plans;
    Locating Optimum Responses, 600
    Exercises, 606xviii CONTENTS
  18. Model Assessment 614
    18.1. Outlier Detection, 614
    18.1.1. Univariate Techniques, 615
    18.1.2. Response-Variable Outliers, 619
    18.1.3. Predictor-Variable Outliers, 626
    18.2. Evaluating Model Assumptions, 630
    18.2.1. Normally Distributed Errors, 630
    18.2.2. Correct Variable Specification, 634
    18.2.3. Nonstochastic Predictor Variables, 637
    18.3. Model Respecification, 639
    18.3.1. Nonlinear-Response Functions, 640
    18.3.2. Power Reexpressions, 642
    Appendix: Calculation of Leverage Values
    and Outlier Diagnostics, 647
    Exercises, 651
  19. Variable Selection Techniques 659
    19.1. Comparing Fitted Models, 660
    19.2. All-Possible-Subset Comparisons, 662
    19.3. Stepwise Selection Methods, 665
    19.3.1. Forward Selection, 666
    19.3.2. Backward Elimination, 668
    19.3.3. Stepwise Iteration, 670
    19.4. Collinear Effects, 672
    Appendix: Cryogenic-Flowmeter Data, 674
    Exercises, 678
    APPENDIX: Statistical Tables 689
  20. Table of Random Numbers, 690
  21. Standard Normal Cumulative Probabilities, 692
  22. Student t Cumulative Probabilities, 693
  23. Chi-Square Cumulative Probabilities, 694
  24. F Cumulative Probabilities, 695
  25. Factors for Determining One-sided Tolerance
    Limits, 701
  26. Factors for Determining Two-sided Tolerance
    Limits, 702xix
  27. Upper-Tail Critical Values for the F-Max
    Test, 703
  28. Orthogonal Polynomial Coefficients, 705
  29. Critical Values for Outlier Test Using
    Lk and Sk, 709
  30. Critical Values for Outlier Test Using Ek, 711
  31. Coefficients Used in the Shapiro–Wilk Test for
    Normality, 713
  32. Critical Values for the Shapiro–Wilk Test for
    Normality, 716
  33. Percentage Points of the Studentized Range, 718
    INDEX 72
    Index
    Added factors, 260
    Adjacent value, 70
    Adjusted factor-level average, 362
    analysis of covariance, 551, 555, 556
    Alias, 230, 319, 324
    All-possible subset comparisons, 662
    Alternative hypothesis, 52, 55
    Analysis of covariance (ANACOVA),
    535, 543
    Analysis of marginal means, 276
    Analysis of variance (ANOVA), 481, 503
    model, 173
    table, 176, 481, 504, 546
    Assignable causes, 173
    Assumptions
    analysis of covariance model, 544, 554
    fixed effects analysis of variance
    model, 173
    linear regression analysis, 463, 481
    random effects analysis of variance
    model, 349
    Average, 33
    Backward elimination, 668
    Balance, 145, 248, 252
    Balanced incomplete block design (BIB),
    325, 357
    Balancing, 316
    Bartlett’s test, 98
    Bias measurement, 402
    Block, 110, 316
    Block design, 311, 317, 318, 400, 552
    complete, 317, 356
    incomplete, 318, 357
    Bonferroni comparisons, 211
    Box–Behnken design, 248, 585
    Box–Cox procedure, 642
    Boxplot comparisons, 70
    Cm (Cp)statistic, 661
    Canonical analysis, 593, 604
    Capability study, 404
    Carryover effects, 331
    Categorical variable, 536, 539
    Central composite design, 248, 582
    Central limit property, 47
    Chi-square probability distribution, 46,
    62, 82
    Coding, 541, 578
    Coefficient of determination, 482, 504,
    661
    adjusted, 505, 661
    Collinear predictors, 518
    Collinearity detection, 672
    Combined array design, 594
    Complete block design, 317, 356
    Completely randomized design, 141,
    170, 229, 542
    three-level, 247
    two-level, 239
    Comprehensive regression analysis, 470
    Computer-generated design, 580
    Confidence coefficient, 75
    Confidence interval, 49
    equivalence to hypothesis test, 78
    for analysis of variance model, 186
    for factor level means, 275
    for normal distribution parameters, 49,
    76, 83, 92, 94
    for ratio of expected mean squares,
    355
    723
    Statistical Design and Analysis of Experiments: With Applications to Engineering and Science,
    Second Edition
    Robert L. Mason, Richard F. Gunst and James L. Hess
    Copyright ¶ 2003 John Wiley & Sons, Inc.
    ISBN: 0-471-37216-1724 INDEX
    Confidence interval (continued)
    for regression model parameters, 484,
    510
    for regression model response mean,
    485, 524
    interpretation, 50, 75
    simultaneous, 524
    Confidence level, 55
    Confounding, 112, 318
    effects, 229
    partial, 320
    pattern, 233, 281, 287
    Constrained factor space, 588
    Contrast, 161, 197, 230
    orthogonal, 198
    sum of squares, 200
    Correlation coefficient, 468
    Covariate, 110, 542
    Criteria for comparing fitted models,
    661
    Critical value, 55
    Crossed array design, 594
    Crossover design, 331
    Curvature, 413
    Data, 4
    collection, 4
    Defining contrast, 239, 319, 324
    Defining equation, 239, 321
    Degrees of freedom, 46, 73, 90, 180
    Density, 20, 42
    Design problems
    erroneous efficiency, 119
    error variation, 115
    masked factors, 115
    one-factor-at-a-time, 121
    uncontrolled factors, 117
    Design resolution, 237
    Design selection criteria
    efficiency, 127
    factor effects, 126
    objective, 125
    precision, 127
    randomization, 128
    Deviations, 35
    DFBETAS, 625
    DFFITS, 625
    Discrimination, 402
    Distribution, 19
    frequency, 21
    normal, 20
    sampling, 21, 45
    Dot notation, 153
    Dual response model, 598
    Effects, 110
    calculation of, 152, 156, 160
    coding of factor levels, 154
    confounded, 230
    fixed, 171
    graphical assessment, 158
    interaction, 153, 175
    joint factor, 145, 178
    linear, 290
    main, 153
    parameters, 277
    plot, 280
    polynomial, 190
    quadratic, 290
    random, 171, 347, 424
    representation, 153
    Effects sum of squares, see Sum of
    squares
    Error mean square (MSE), 185, 273,
    482, 504
    Error rates
    comparisonwise, 201
    experimentwise, 201
    type I, 201
    type II, 202
    Error standard deviation, 184
    Estimate, 44
    Estimated error standard deviation, 73,
    157, 276, 482, 504
    Estimated experimental error, 185
    Evolutionary operation (EVOP), 130
    Expected mean square, 350, 366, 425
    Experimental error, 411
    Experimental layout, 112
    Experimental region, 110, 575
    Experimental studies, 4
    Experimental unit, 110
    F probability distribution, 46, 62
    F ratio, 46, 93, 195, 661
    F statistic, 93
    Face-centered cube design, 583
    Factor, 12
    Factor effects, see Effects, 171
    Factor levels, 110, 189
    quantitative, 189
    random, 347
    space, 111INDEX 725
    Factorial experiments, 141, 228, 580
    Factors, 12
    balanced, 382
    control, 408, 598
    crossed, 379
    environmental, 408
    hard to vary, 391
    nested, 379
    noise, 598
    uncontrolled, 117
    F-max test, 97
    Fold-over designs, 260
    Forward selection, 666
    Fractional factorial, 228, 321
    Fractional factorial experiment, 144,
    228, 278, 287, 290, 580
    analysis of, 278, 287, 290
    French curve, 516
    Gage R&R studies, 401, 433
    Graeco-Latin-Square design, 330
    Grouping, 316
    Grubbs test, 617
    Hierarchical model, see Model
    Hierarchically nested designs, 381, 423
    Histogram
    relative-frequency, 22
    Hybrid design, 588
    Hypothesis tests
    analysis of covariance model
    parameters, 544
    analysis of variance model parameters,
    194, 275
    decision rules, 77
    for factor effects, 195
    for normal distribution parameters, 52,
    78, 85, 92, 95
    lack of fit, 506
    p-value calculations, 77
    regression model parameters, 484, 508
    Hypothesis types, 52
    Incomplete block design, 318, 357
    balanced, 325
    three-level factorial, 323
    two-level factorial, 318
    Independence, 44
    Indicator variables, 461, 536
    Inferences
    on means, 72, 86, 89
    on standard deviations two samples,
    81, 93
    on regression models, 481, 503
    Influential observations, 624
    Inner array, 408
    Integrated approach, 410
    Integrated design model, 598
    Interaction, 110, 146, 511, 541
    Interaction plot, 216
    Lack-of-fit
    error, 482, 506
    test, 506
    Latin-square design, 328, 364
    Least significant
    difference, 210
    interval, 218
    Least squares estimation, 475, 478, 480,
    497
    interpretation, 478, 499
    Least squares fit, 476
    Least squares means, 278
    Leverage values, 628
    Local control, 316
    Loess smoothing, 474
    Masking, 115, 618
    Mean, 33
    Mean square, 181
    Expected, 350, 366, 425
    Measurement process, 401
    Measurement variation, 6, 402
    Median, 34
    Mixed-levels designs, 254
    Mixture design, 588
    Model
    analysis of covariance, 543, 553
    analysis of variance, 173
    assumptions, 630
    extrapolation, 463, 518
    first-order, 513, 515
    fixed effects, 173, 348, 429
    hierarchical, 176, 272
    integrated design, 587
    linear, 462, 497, 536
    mathematical, 25
    no-intercept regression, 480, 485
    nonlinear, 640
    one-way classification, 184
    order, 513, 515
    polynomial, 514, 588726 INDEX
    Model (continued)
    random-effect, 349
    regression, 462, 497, 536
    respecification, 639
    response surface, 588
    saturated, 185
    second-order, 513, 515
    specification, 462, 472, 497, 634
    statistical, 25
    sum of squares, see Sum of squares
    Multi-panel conditioning, 214
    Multiple comparison procedures, 196
    Nested design, 378, 423
    Nested factors, see Factor
    Noncentral composite design, 588
    Nonlinear
    relationship, 635, 640
    response function, 640
    Nonorthogonal designs, 252
    Normal density function, 43
    Normal equations, 499
    Normal probability distribution, 20, 43,
    59
    Null hypothesis, 52, 55
    Observation, 12
    Observational
    data, 587
    studies, 4
    Observed value, 11
    One-Factor-at-a-Time (OFAT) Testing,
    121
    Operating characteristic curve, 59, 80
    Optimum response, 573, 576
    Orthogonal arrays, 252, 407, 414
    Orthogonal contrast, see Contrast
    Orthogonal polynomials, 207
    Outer array, 408
    Outliers, 70
    accommodation, 615
    detection, 614
    in predictor variables, 626
    in response variables, 619
    Parameter, 19
    analysis of variance model, 174
    constraints, 174
    estimation, 186
    interaction, 174
    main-effect, 174
    Parsimony, 516
    Partial regression coefficient estimate,
    499
    Pearson’s r, 468
    Pick the winner, 437, 457
    PISEAS, 470
    Plackett–Burman design, 256
    analysis, 293
    Plots
    boxplot, 70
    contour, 122, 571
    cube, 213
    factor effects, 158
    interaction, 150, 216
    labeled scatterplot, 148
    least significant interval, 218
    normal quantile-quantile, 159, 630
    overlaying, 575
    partial-regression, 637
    partial-residual, 635
    point, 39
    residual, 634
    scatter, 6, 148
    studentized deleted residual, 644
    trellis, 214
    Pooled standard deviation estimate, 90
    Population, 10
    Power, 56
    Precision, 127
    Prediction
    equation, 475, 498
    interval, 485
    Probability concepts, 42
    Product array design, 594
    Process, 10
    capability, 404
    Pure error, 506
    p-value, 55, 77
    Quadratic model, 515, 588
    Quality control procedures, 128
    Quality loss function, 407
    Quantile, 159
    Quartile, 37
    Random sample, 14
    Randomization, 128, 142, 391
    restricted, 391
    Randomized complete block (RCB)
    design, 317, 552
    Range, 35INDEX 727
    Reduction in error sum of squares,
    273
    Reexpression, 642, 647
    Regression analysis
    assumptions, 463, 481
    common uses and misuses, 462
    analysis linear, 470
    local fit, 473
    strategy, 470
    sum of squares, 481, 503
    Regression coefficient, 462, 497
    beta-weight, 502, 519
    standardized, 502, 519
    Regression fallacy, 480
    Repeat test, 110, 144, 312
    Repeatability, 315, 402, 434
    Replication, 110, 312
    Reproducibility, 315, 402, 434
    Residuals, 475, 498
    partial, 635
    studentized deleted, 623
    Response
    dispersion, 130
    location, 130
    predicted, 475, 498
    variable, 120
    Response surface designs, 129, 410, 568,
    580
    Box–Behnken, 413, 585
    central composite, 413, 582
    Rising ridge, 572
    Robust design, 401
    parameter design, 587, 594
    Robustness, 401
    Rotatable design, 581
    Ruggedness tests, 267, 293
    Saddle, 572
    Sample correlation coefficient, 468
    Sample, 13
    mean 34
    sampling distribution of, 45
    median, 34
    size, 56, 79
    standard deviation, 36, 73
    types of, 13
    variance, 46
    Sampling distribution, 21, 45, 73
    Saturated designs, 253
    Scatterplot 6; smoothing, 473
    Screening design, 144, 256
    analysis, 293
    Screening experiments, 129, 158, 256
    Semi-interquartile range, 37, 70
    Sequential experimentation, 255, 331
    Shapiro–Wilk test for normality, 633
    Signal-to-noise ratio, 436
    Significance level, 55
    Significance probability, 55
    Simplex design, 588
    Small composite design, 588
    Smoothing, 473
    Span, 473
    Split plot, 384, 388
    Split-plot design, 384, 388, 428
    Stable process, 404
    Staggered nested design, 382, 427
    Standard deviation, 36, 81
    Standard error, 45
    Standard normal variate, 44
    Standard process, 404
    Standardized predictor variable, 519,
    591
    Stationary point, 593
    Stationary ridge, 571
    Statistic, 4, 19
    Steepest ascent method, 602
    Stepwise variable selection techniques,
    665
    collinear effects, 672
    Student t distribution, 46, 60
    approximate, 91
    Sum of squares
    contrast, 200
    error, 180, 481, 498
    interaction effect, 178
    main effect, 178
    model, 177
    partitioned, 177
    regression, 481, 503
    total, 177, 481
    Supersaturated design analysis, 297
    Taguchi approach, 129, 406
    Taguchi design, 406, 436
    t-distribution, 46
    Test run, 110
    Tolerance intervals, 50
    Transformation
    Box–Cox, 642
    logarithmic, 640
    power-family, 642
    Transmitted variation, 411
    t-statistic, 73, 209728 INDEX
    Tukey’s significant difference, 212
    Type I error, 55, 202
    Type II error, 55, 202
    Unbalanced design
    analysis, 272
    Variable 11
    categorical, 536
    collinear, 518
    continuous, 42
    indicator, 461, 536
    predictor, 461, 462, 497
    response, 12, 110
    selection techniques, 659
    standardized, 579
    Variance component, 350, 434
    Variance inflation factors, 673
    Variation
    assignable cause, 173
    measurement, 402
    random, 173
    sources of, 173
    transmitted, 411
    Whole plots, 388

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