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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 						

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