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

اسم المؤلف

Robert L. Mason, Richard F. Gunst, James L. Hess

التاريخ

تاريخ النشر9 نوفمبر 2021

التصنيف

فيهندسة الإنتاج والتصميم الميكانيكى

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260

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(لا توجد تقييمات)

التحميل

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

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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Table of Random Numbers, 690
Standard Normal Cumulative Probabilities, 692
Student t Cumulative Probabilities, 693
Chi-Square Cumulative Probabilities, 694
F Cumulative Probabilities, 695
Factors for Determining One-sided Tolerance
Limits, 701
Factors for Determining Two-sided Tolerance
Limits, 702xix
Upper-Tail Critical Values for the F-Max
Test, 703
Orthogonal Polynomial Coefficients, 705
Critical Values for Outlier Test Using
Lk and Sk, 709
Critical Values for Outlier Test Using Ek, 711
Coefficients Used in the Shapiro–Wilk Test for
Normality, 713
Critical Values for the Shapiro–Wilk Test for
Normality, 716
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