MasonGunstHess 2003 - Statistical design and analysis of experiments with applications to engineering and science

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PART I FUNDAMENTAL STATISTICAL CONCEPTS1
1.Statistics in Engineering and Science3
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 Inference33
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

3.Inferences on Means and Standard Deviations69
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
STRUCTURE107
4.Statistical Principles in Experimental Design109
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,132

5.Factorial Experiments in Completely Randomized
Designs140
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 Designs170
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 Experiments228
7.1.Confounding of Factor Effects,229
7.2.Design Resolution,237
7.3.Two-Level Fractional Factorial Experiments,239
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 Experiments271
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 Effects309
9.Experiments in Randomized Block Designs311
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,325
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 Levels347
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 Designs378
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 Improvement400
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,418

13.Analysis of Nested Designs and Designs for Process
Improvement423
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 Factors459
14.Linear Regression with One Predictor Variable461
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 Variables496
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,510
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 Predictors535
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 Surfaces568
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,606

18.Model Assessment614
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 Techniques659
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 Tables689
1.Table of Random Numbers,690
2.Standard Normal Cumulative Probabilities,692
3.Student t Cumulative Probabilities,693
4.Chi-Square Cumulative Probabilities,694
5.F Cumulative Probabilities,695
6.Factors for Determining One-sided Tolerance
Limits,701
7.Factors for Determining Two-sided Tolerance
Limits,702