Contents
Inside Front cover Index of Applications
Examples and Exercises
Chapter 1 The Role of Statistics in Engineering 1
1-1 The Engineering Method and Statistical
Thinking 2
1-2 Collecting Engineering Data 4
1-2.1 Basic Principles 4
1-2.2 Retrospective Study 5
1-2.3 Observational Study 5
1-2.4 Designed Experiments 6
1-2.5 Observing Processes Over Time 8
1-3 Mechanistic and Empirical Models 11
1-4 Probability and Probability Models 12
Chapter 2 Probability 15
2-1 Sample Spaces and Events 16
2-1.1 Random Experiments 16
2-1.2 Sample Spaces 17
2-1.3 Events 20
2-1.4 Counting Techniques 22
2-2 Interpretations and Axioms of Probability 30
2-3 Addition Rules 35
2-4 Conditional Probability 40
2-5 Multiplication and Total Probability
Rules 45
2-6 Independence 49
#BZFT5IFPSFN
2-8 Random Variables 57
Chapter 3 Discrete Random Variables and
Probability Distributions 65
3-1 Discrete Random Variables 66
3-2 Probability Distributions and Probability Mass
Functions 67
3-3 Cumulative Distribution Functions 71
3-4 Mean and Variance of a Discrete Random
Variable 74
3-5 Discrete Uniform Distribution 78
3-6 Binomial Distribution 80
3-7 Geometric and Negative Binomial
Distributions 86
3-7.1 Geometric Distribution 86
3-8 Hypergeometric Distribution 93
3-9 Poisson Distribution 98
Chapter 4 Continuous Random Variables
and Probability Distributions 107
4-1 Continuous Random Variables 108
4-2 Probability Distributions and Probability
Density Functions 108
4-3 Cumulative Distribution Functions 112
4-4 Mean and Variance of a Continuous
Random Variable 114
4-5 Continuous Uniform Distribution 116
4-6 Normal Distribution 119
4-7 Normal Approximation to the Binomial and
Poisson Distributions 128
4-8 Exponential Distribution 133
4-9 Erlang and Gamma Distributions 139
4-10 Weibull Distribution 143
4-11 Lognormal Distribution 145
4-12 Beta Distribution 148
Chapter 5 Joint Probability Distributions 155
5-1 Two or More Random Variables 156
5-1.1 Joint Probability Distributions 156
5-1.2 Marginal Probability Distributions 159
5-1.3 Conditional Probability Distributions 161
5-1.4 Independence 164
5-1.5 More Than Two Random Variables 167
5-2 Covariance and Correlation 174
5-3 Common Joint Distributions 179
5-3.1 Multinomial Probability Distribution 179
5-3.2 Bivariate Normal Distribution 181
5-4 Linear Functions of Random Variables 184
5-5 General Functions of Random Variables 188
5-6 Moment-Generating Functions 191
Chapter 6 Descriptive Statistics 199
6-1 Numerical Summaries of Data 200
6-2 Stem-and-Leaf Diagrams 206
6-3 Frequency Distributions and Histograms 213
6-4 Box Plots 217
6-5 Time Sequence Plots 219
6-6 Scatter Diagrams 225
6-7 Probability Plots 230
Chapter 7 Point Estimation of Parameters and
Sampling Distributions 239
7-1 Point Estimation 240
fm.indd 14 9/26/2013 11:53:56 AM
Contents xv
7-2 Sampling Distributions
and the Central Limit Theorem 241
7-3 General Concepts of Point Estimation 249
7-3.1 Unbiased Estimators 249
7-3.2 Variance of a Point Estimator 251
7-3.3 Standard Error: Reporting a Point
Estimate 251
7.3.4 Bootstrap Standard Error 252
7-3.5 Mean Squared Error of an Estimator 254
7-4 Methods of Point Estimation 256
7-4.1 Method of Moments 256
7-4.2 Method of Maximum Likelihood 258
7-4.3 Bayesian Estimation of
Parameters 264
Chapter 8 Statistical Intervals for a
Single Sample 271
8-1 Confidence Interval on the Mean of a Normal
Distribution, Variance Known 273
8-1.1 Development of the Confidence Interval
and Its Basic Properties 273
8-1.2 Choice of Sample Size 276
8-1.3 One-Sided Confidence Bounds 277
8-1.4 General Method to Derive a Confidence
Interval 277
8-1.5 Large-Sample Confidence Interval
for μ 279
8-2 Confidence Interval on the Mean of a Normal
Distribution, Variance Unknown 282
8-2.1 t Distribution 283
8-2.2 t Confidence Interval on μ 284
8-3 Confidence Interval on the Variance and
Standard Deviation of a Normal
Distribution 287
8-4 Large-Sample Confidence Interval
for a Population Proportion 291
8-5 Guidelines for Constructing Confidence
Intervals 296
8.6 Bootstrap Confidence Interval 296
8-7 Tolerance and Prediction Intervals 297
8-7.1 Prediction Interval for a Future
Observation 297
8-7.2 Tolerance Interval for a Normal
Distribution 298
Chapter 9 Tests of Hypotheses for a
Single Sample 305
9-1 Hypothesis Testing 306
9-1.1 statistical hypotheses 306
9-1.2 Tests of Statistical Hypotheses 308
9-1.3 One-Sided and Two-Sided
Hypotheses 313
9-1.4 P-Values in Hypothesis Tests 314
9-1.5 Connection Between Hypothesis Tests
and Confidence Intervals 316
9-1.6 General Procedure for Hypothesis
Tests 318
9-2 Tests on the Mean of a Normal Distribution,
Variance Known 322
9-2.1 Hypothesis Tests on the Mean 322
9-2.2 Type II Error and Choice of Sample
Size 325
9-2.3 Large-Sample Test 329
9-3 Tests on the Mean of a Normal Distribution,
Variance Unknown 331
9-3.1 Hypothesis Tests on the Mean 331
9-3.2 Type II Error and Choice of Sample
Size 336
9-4 Tests on the Variance and Standard
Deviation of a Normal Distribution 340
9-4.1 Hypothesis Tests on the Variance 341
9-4.2 Type II Error and Choice of Sample
Size 343
9-5 Tests on a Population Proportion 344
9-5.1 Large-Sample Tests on a Proportion 344
9-5.2 Type II Error and Choice of Sample
Size 347
9-6 Summary Table of Inference Procedures
for a Single Sample 350
9-7 Testing for Goodness of Fit 350
9-8 Contingency Table Tests 354
9-9 Nonparametric Procedures 357
9-9.1 The Sign Test 358
9-9.2 The Wilcoxon Signed-Rank Test 362
9-9.3 Comparison to the t-Test 364
9-10 Equivalence Testing 365
9-11 Combining P-Values 367
Chapter 10 Statistical Inference for
Two Samples 373
10-1 Inference on the Difference in Means of Two
Normal Distributions, Variances Known 374
10-1.1 Hypothesis Tests on the Difference in
Means, Variances Known 376
10-1.2 Type II Error and Choice of Sample
Size 377
10-1.3 Confidence Interval on the Difference in
Means, Variances Known 379
10-2 Inference on the Difference in Means of two
Normal Distributions, Variances Unknown 383
fm.indd 15 9/26/2013 11:53:56 AM
xvi Contents
10-2.1 Hypotheses Tests on the Difference in
Means, Variances Unknown 383
10-2.2 Type II Error and Choice of Sample
Size 389
10-2.3 Confidence Interval on the Difference in
Means, Variances Unknown 390
10-3 A Nonparametric Test for the Difference in Two
Means 396
10-3.1 Description of the Wilcoxon Rank-Sum
Test 397
10-3.2 Large-Sample Approximation 398
10-3.3 Comparison to the t-Test 399
10-4 Paired t-Test 400
10-5 Inference on the Variances of Two Normal
Distributions 407
10-5.1 F Distribution 407
10-5.2 Hypothesis Tests on the Ratio of Two
Variances 409
10-5.3 Type II Error and Choice of Sample
Size 411
10-5.4 Confidence Interval on the Ratio of Two
Variances 412
10-6 Inference on Two Population
Proportions 414
10-6.1 Large-Sample Tests on the Difference in
Population Proportions 414
10-6.2 Type II Error and Choice of Sample
Size 416
10-6.3 Confidence Interval on the Difference in
Population Proportions 417
10-7 Summary Table and Road Map for Inference
Procedures for Two Samples 420
Chapter 11 Simple Linear Regression
and Correlation 427
11-1 Empirical Models 428
11-2 Simple Linear Regression 431
11-3 Properties of the Least Squares
Estimators 440
11-4 Hypothesis Tests in Simple Linear
Regression 441
11-4.1 Use of t-Tests 441
11-4.2 Analysis of Variance Approach to Test
Significance of Regression 443
11-5 Confidence Intervals 447
11-5.1 Confidence Intervals on the Slope and
Intercept 447
11-5.2 Confidence Interval on the Mean
Response 448
11-6 Prediction of New Observations 449
11-7 Adequacy of the Regression Model 452
11-7.1 Residual Analysis 453
11-7.2 Coefficient of Determination
(R2
) 454
11-8 Correlation 457
11-9 Regression on Transformed Variables 463
11-10 Logistic Regression 467
Chapter 12 Multiple Linear Regression 477
12-1 Multiple Linear Regression Model 478
12-1.1 Introduction 478
12-1.2 Least Squares Estimation of the
Parameters 481
12-1.3 Matrix Approach to Multiple Linear
Regression 483
12-1.4 Properties of the Least Squares
Estimators 488
12-2 Hypothesis Tests In Multiple Linear
Regression 497
12-2.1 Test for Significance
of Regression 497
12-2.2 Tests on Individual Regression
Coefficients and Subsets of
Coefficients 500
12-3 Confidence Intervals In Multiple Linear
Regression 506
12-3.1 Confidence Intervals on Individual
Regression Coefficients 506
12-3.2 Confidence Interval on the Mean
Response 507
12-4 Prediction of New Observations 508
12-5 Model Adequacy Checking 511
12-5.1 Residual Analysis 511
12-5.2 Influential Observations 514
12-6 Aspects of Multiple Regression
Modeling 517
12-6.1 Polynomial Regression Models 517
12-6.2 Categorical Regressors and Indicator
Variables 519
12-6.3 Selection of Variables and Model
Building 522
12-6.4 Multicollinearity 529
Chapter 13 Design and Analysis of Single-Factor
Experiments: The Analysis of Variance 539
13-1 Designing Engineering Experiments 540
13-2 Completely Randomized Single-Factor
Experiment 541
13-2.1 Example: Tensile Strength 541
13-2.2 Analysis of Variance 542
13-2.3 Multiple Comparisons Following the
ANOVA 549
fm.indd 16 9/26/2013 11:53:56 AM
Contents xvii
13-2.4 Residual Analysis and Model
Checking 551
13-2.5 Determining Sample Size 553
13-3 The Random-Effects Model 559
13-3.1 Fixed Versus Random Factors 559
13-3.2 ANOVA and Variance Components 560
13-4 Randomized Complete Block Design 565
13-4.1 Design and Statistical Analysis 565
13-4.2 Multiple Comparisons 570
13-4.3 Residual Analysis and Model
Checking 571
Chapter 14 Design of Experiments with Several
Factors 575
14-1 Introduction 576
14-2 Factorial Experiments 578
14-3 Two-Factor Factorial Experiments 582
14-3.1 Statistical Analysis of the Fixed-Effects
Model 582
14-3.2 Model Adequacy Checking 587
14-3.3 One Observation per Cell 588
14-4 General Factorial Experiments 591
14-5 2k
Factorial Designs 594
14-5.1 22
Design 594
14-5.2 2k Design for k≥3 Factors 600
14-5.3 Single Replicate of the 2k
Design 607
14-5.4 Addition of Center Points to
a 2k
Design 611
14-6 Blocking and Confounding in the 2k
Design 619
14-7 Fractional Replication of the 2k
Design 626
14-7.1 One-Half Fraction of the
2k
Design 626
14-7.2 Smaller Fractions: The 2k–p Fractional
Factorial 632
14-8 Response Surface Methods and Designs 643
Chapter 15 Statistical Quality Control 663
15-1 Quality Improvement and Statistics 664
15-1.1 Statistical Quality Control 665
15-1.2 Statistical Process Control 666
15-2 Introduction to Control Charts 666
15-2.1 Basic Principles 666
15-2.2 Design of a Control Chart 670
15-2.3 Rational Subgroups 671
15-2.4 Analysis of Patterns on Control Charts
672
15-3 X
–
and R or S Control Charts 674
15-4 Control Charts for Individual
Measurements 684
15-5 Process Capability 692
15-6 Attribute Control Charts 697
15-6.1 P Chart (Control Chart for
Proportions) 697
15-6.2 U Chart (Control Chart for Defects per
Unit) 699
15-7 Control Chart Performance 704
15-8 Time-Weighted Charts 708
15-8.1 Cumulative Sum Control Chart 709
15-8.2 Exponentially Weighted Moving-
Average Control Chart 714
15-9 Other SPC Problem-Solving Tools 722
15-10 Decision Theory 723
15-10.1 Decision Models 723
15-10.2 Decision Criteria 724
15-11 Implementing SPC 726
Appendix A. Statistical Tables and Charts 737
Table I Summary of Common Probability
Distributions 738
Table II Cumulative Binomial Probabilities
PX x ( ) ≤ 739
Table III Cumulative Standard Normal
Distribution 742
Table IV Percentage Points χα,v
2 of the Chi-Squared
Distribution 744
Table V Percentage Points tα,v of the t
Distribution 745
Table VI Percentage Points fα, , v v 1 2 of the F
Distribution 746
Chart VII Operating Characteristic Curves 751
Table VIII Critical Values for the Sign Test 760
Table IX Critical Values for the Wilcoxon Signed-Rank
Test 760
Table X Critical Values for the Wilcoxon Rank-Sum
Test 761
Table XI Factors for Constructing Variables Control
Charts 762
Table XII Factors for Tolerance Intervals 762
Appendix B: Bibliography 765
Appendix C: Answers to Selected Exercises 769
Glossary 787
Index 803
Index of applications in examples and
exercises, continued 809
Inside Front cover Index of Applications
Examples and Exercises
Chapter 1 The Role of Statistics in Engineering 1
1-1 The Engineering Method and Statistical
Thinking 2
1-2 Collecting Engineering Data 4
1-2.1 Basic Principles 4
1-2.2 Retrospective Study 5
1-2.3 Observational Study 5
1-2.4 Designed Experiments 6
1-2.5 Observing Processes Over Time 8
1-3 Mechanistic and Empirical Models 11
1-4 Probability and Probability Models 12
Chapter 2 Probability 15
2-1 Sample Spaces and Events 16
2-1.1 Random Experiments 16
2-1.2 Sample Spaces 17
2-1.3 Events 20
2-1.4 Counting Techniques 22
2-2 Interpretations and Axioms of Probability 30
2-3 Addition Rules 35
2-4 Conditional Probability 40
2-5 Multiplication and Total Probability
Rules 45
2-6 Independence 49
#BZFT5IFPSFN
2-8 Random Variables 57
Chapter 3 Discrete Random Variables and
Probability Distributions 65
3-1 Discrete Random Variables 66
3-2 Probability Distributions and Probability Mass
Functions 67
3-3 Cumulative Distribution Functions 71
3-4 Mean and Variance of a Discrete Random
Variable 74
3-5 Discrete Uniform Distribution 78
3-6 Binomial Distribution 80
3-7 Geometric and Negative Binomial
Distributions 86
3-7.1 Geometric Distribution 86
3-8 Hypergeometric Distribution 93
3-9 Poisson Distribution 98
Chapter 4 Continuous Random Variables
and Probability Distributions 107
4-1 Continuous Random Variables 108
4-2 Probability Distributions and Probability
Density Functions 108
4-3 Cumulative Distribution Functions 112
4-4 Mean and Variance of a Continuous
Random Variable 114
4-5 Continuous Uniform Distribution 116
4-6 Normal Distribution 119
4-7 Normal Approximation to the Binomial and
Poisson Distributions 128
4-8 Exponential Distribution 133
4-9 Erlang and Gamma Distributions 139
4-10 Weibull Distribution 143
4-11 Lognormal Distribution 145
4-12 Beta Distribution 148
Chapter 5 Joint Probability Distributions 155
5-1 Two or More Random Variables 156
5-1.1 Joint Probability Distributions 156
5-1.2 Marginal Probability Distributions 159
5-1.3 Conditional Probability Distributions 161
5-1.4 Independence 164
5-1.5 More Than Two Random Variables 167
5-2 Covariance and Correlation 174
5-3 Common Joint Distributions 179
5-3.1 Multinomial Probability Distribution 179
5-3.2 Bivariate Normal Distribution 181
5-4 Linear Functions of Random Variables 184
5-5 General Functions of Random Variables 188
5-6 Moment-Generating Functions 191
Chapter 6 Descriptive Statistics 199
6-1 Numerical Summaries of Data 200
6-2 Stem-and-Leaf Diagrams 206
6-3 Frequency Distributions and Histograms 213
6-4 Box Plots 217
6-5 Time Sequence Plots 219
6-6 Scatter Diagrams 225
6-7 Probability Plots 230
Chapter 7 Point Estimation of Parameters and
Sampling Distributions 239
7-1 Point Estimation 240
fm.indd 14 9/26/2013 11:53:56 AM
Contents xv
7-2 Sampling Distributions
and the Central Limit Theorem 241
7-3 General Concepts of Point Estimation 249
7-3.1 Unbiased Estimators 249
7-3.2 Variance of a Point Estimator 251
7-3.3 Standard Error: Reporting a Point
Estimate 251
7.3.4 Bootstrap Standard Error 252
7-3.5 Mean Squared Error of an Estimator 254
7-4 Methods of Point Estimation 256
7-4.1 Method of Moments 256
7-4.2 Method of Maximum Likelihood 258
7-4.3 Bayesian Estimation of
Parameters 264
Chapter 8 Statistical Intervals for a
Single Sample 271
8-1 Confidence Interval on the Mean of a Normal
Distribution, Variance Known 273
8-1.1 Development of the Confidence Interval
and Its Basic Properties 273
8-1.2 Choice of Sample Size 276
8-1.3 One-Sided Confidence Bounds 277
8-1.4 General Method to Derive a Confidence
Interval 277
8-1.5 Large-Sample Confidence Interval
for μ 279
8-2 Confidence Interval on the Mean of a Normal
Distribution, Variance Unknown 282
8-2.1 t Distribution 283
8-2.2 t Confidence Interval on μ 284
8-3 Confidence Interval on the Variance and
Standard Deviation of a Normal
Distribution 287
8-4 Large-Sample Confidence Interval
for a Population Proportion 291
8-5 Guidelines for Constructing Confidence
Intervals 296
8.6 Bootstrap Confidence Interval 296
8-7 Tolerance and Prediction Intervals 297
8-7.1 Prediction Interval for a Future
Observation 297
8-7.2 Tolerance Interval for a Normal
Distribution 298
Chapter 9 Tests of Hypotheses for a
Single Sample 305
9-1 Hypothesis Testing 306
9-1.1 statistical hypotheses 306
9-1.2 Tests of Statistical Hypotheses 308
9-1.3 One-Sided and Two-Sided
Hypotheses 313
9-1.4 P-Values in Hypothesis Tests 314
9-1.5 Connection Between Hypothesis Tests
and Confidence Intervals 316
9-1.6 General Procedure for Hypothesis
Tests 318
9-2 Tests on the Mean of a Normal Distribution,
Variance Known 322
9-2.1 Hypothesis Tests on the Mean 322
9-2.2 Type II Error and Choice of Sample
Size 325
9-2.3 Large-Sample Test 329
9-3 Tests on the Mean of a Normal Distribution,
Variance Unknown 331
9-3.1 Hypothesis Tests on the Mean 331
9-3.2 Type II Error and Choice of Sample
Size 336
9-4 Tests on the Variance and Standard
Deviation of a Normal Distribution 340
9-4.1 Hypothesis Tests on the Variance 341
9-4.2 Type II Error and Choice of Sample
Size 343
9-5 Tests on a Population Proportion 344
9-5.1 Large-Sample Tests on a Proportion 344
9-5.2 Type II Error and Choice of Sample
Size 347
9-6 Summary Table of Inference Procedures
for a Single Sample 350
9-7 Testing for Goodness of Fit 350
9-8 Contingency Table Tests 354
9-9 Nonparametric Procedures 357
9-9.1 The Sign Test 358
9-9.2 The Wilcoxon Signed-Rank Test 362
9-9.3 Comparison to the t-Test 364
9-10 Equivalence Testing 365
9-11 Combining P-Values 367
Chapter 10 Statistical Inference for
Two Samples 373
10-1 Inference on the Difference in Means of Two
Normal Distributions, Variances Known 374
10-1.1 Hypothesis Tests on the Difference in
Means, Variances Known 376
10-1.2 Type II Error and Choice of Sample
Size 377
10-1.3 Confidence Interval on the Difference in
Means, Variances Known 379
10-2 Inference on the Difference in Means of two
Normal Distributions, Variances Unknown 383
fm.indd 15 9/26/2013 11:53:56 AM
xvi Contents
10-2.1 Hypotheses Tests on the Difference in
Means, Variances Unknown 383
10-2.2 Type II Error and Choice of Sample
Size 389
10-2.3 Confidence Interval on the Difference in
Means, Variances Unknown 390
10-3 A Nonparametric Test for the Difference in Two
Means 396
10-3.1 Description of the Wilcoxon Rank-Sum
Test 397
10-3.2 Large-Sample Approximation 398
10-3.3 Comparison to the t-Test 399
10-4 Paired t-Test 400
10-5 Inference on the Variances of Two Normal
Distributions 407
10-5.1 F Distribution 407
10-5.2 Hypothesis Tests on the Ratio of Two
Variances 409
10-5.3 Type II Error and Choice of Sample
Size 411
10-5.4 Confidence Interval on the Ratio of Two
Variances 412
10-6 Inference on Two Population
Proportions 414
10-6.1 Large-Sample Tests on the Difference in
Population Proportions 414
10-6.2 Type II Error and Choice of Sample
Size 416
10-6.3 Confidence Interval on the Difference in
Population Proportions 417
10-7 Summary Table and Road Map for Inference
Procedures for Two Samples 420
Chapter 11 Simple Linear Regression
and Correlation 427
11-1 Empirical Models 428
11-2 Simple Linear Regression 431
11-3 Properties of the Least Squares
Estimators 440
11-4 Hypothesis Tests in Simple Linear
Regression 441
11-4.1 Use of t-Tests 441
11-4.2 Analysis of Variance Approach to Test
Significance of Regression 443
11-5 Confidence Intervals 447
11-5.1 Confidence Intervals on the Slope and
Intercept 447
11-5.2 Confidence Interval on the Mean
Response 448
11-6 Prediction of New Observations 449
11-7 Adequacy of the Regression Model 452
11-7.1 Residual Analysis 453
11-7.2 Coefficient of Determination
(R2
) 454
11-8 Correlation 457
11-9 Regression on Transformed Variables 463
11-10 Logistic Regression 467
Chapter 12 Multiple Linear Regression 477
12-1 Multiple Linear Regression Model 478
12-1.1 Introduction 478
12-1.2 Least Squares Estimation of the
Parameters 481
12-1.3 Matrix Approach to Multiple Linear
Regression 483
12-1.4 Properties of the Least Squares
Estimators 488
12-2 Hypothesis Tests In Multiple Linear
Regression 497
12-2.1 Test for Significance
of Regression 497
12-2.2 Tests on Individual Regression
Coefficients and Subsets of
Coefficients 500
12-3 Confidence Intervals In Multiple Linear
Regression 506
12-3.1 Confidence Intervals on Individual
Regression Coefficients 506
12-3.2 Confidence Interval on the Mean
Response 507
12-4 Prediction of New Observations 508
12-5 Model Adequacy Checking 511
12-5.1 Residual Analysis 511
12-5.2 Influential Observations 514
12-6 Aspects of Multiple Regression
Modeling 517
12-6.1 Polynomial Regression Models 517
12-6.2 Categorical Regressors and Indicator
Variables 519
12-6.3 Selection of Variables and Model
Building 522
12-6.4 Multicollinearity 529
Chapter 13 Design and Analysis of Single-Factor
Experiments: The Analysis of Variance 539
13-1 Designing Engineering Experiments 540
13-2 Completely Randomized Single-Factor
Experiment 541
13-2.1 Example: Tensile Strength 541
13-2.2 Analysis of Variance 542
13-2.3 Multiple Comparisons Following the
ANOVA 549
fm.indd 16 9/26/2013 11:53:56 AM
Contents xvii
13-2.4 Residual Analysis and Model
Checking 551
13-2.5 Determining Sample Size 553
13-3 The Random-Effects Model 559
13-3.1 Fixed Versus Random Factors 559
13-3.2 ANOVA and Variance Components 560
13-4 Randomized Complete Block Design 565
13-4.1 Design and Statistical Analysis 565
13-4.2 Multiple Comparisons 570
13-4.3 Residual Analysis and Model
Checking 571
Chapter 14 Design of Experiments with Several
Factors 575
14-1 Introduction 576
14-2 Factorial Experiments 578
14-3 Two-Factor Factorial Experiments 582
14-3.1 Statistical Analysis of the Fixed-Effects
Model 582
14-3.2 Model Adequacy Checking 587
14-3.3 One Observation per Cell 588
14-4 General Factorial Experiments 591
14-5 2k
Factorial Designs 594
14-5.1 22
Design 594
14-5.2 2k Design for k≥3 Factors 600
14-5.3 Single Replicate of the 2k
Design 607
14-5.4 Addition of Center Points to
a 2k
Design 611
14-6 Blocking and Confounding in the 2k
Design 619
14-7 Fractional Replication of the 2k
Design 626
14-7.1 One-Half Fraction of the
2k
Design 626
14-7.2 Smaller Fractions: The 2k–p Fractional
Factorial 632
14-8 Response Surface Methods and Designs 643
Chapter 15 Statistical Quality Control 663
15-1 Quality Improvement and Statistics 664
15-1.1 Statistical Quality Control 665
15-1.2 Statistical Process Control 666
15-2 Introduction to Control Charts 666
15-2.1 Basic Principles 666
15-2.2 Design of a Control Chart 670
15-2.3 Rational Subgroups 671
15-2.4 Analysis of Patterns on Control Charts
672
15-3 X
–
and R or S Control Charts 674
15-4 Control Charts for Individual
Measurements 684
15-5 Process Capability 692
15-6 Attribute Control Charts 697
15-6.1 P Chart (Control Chart for
Proportions) 697
15-6.2 U Chart (Control Chart for Defects per
Unit) 699
15-7 Control Chart Performance 704
15-8 Time-Weighted Charts 708
15-8.1 Cumulative Sum Control Chart 709
15-8.2 Exponentially Weighted Moving-
Average Control Chart 714
15-9 Other SPC Problem-Solving Tools 722
15-10 Decision Theory 723
15-10.1 Decision Models 723
15-10.2 Decision Criteria 724
15-11 Implementing SPC 726
Appendix A. Statistical Tables and Charts 737
Table I Summary of Common Probability
Distributions 738
Table II Cumulative Binomial Probabilities
PX x ( ) ≤ 739
Table III Cumulative Standard Normal
Distribution 742
Table IV Percentage Points χα,v
2 of the Chi-Squared
Distribution 744
Table V Percentage Points tα,v of the t
Distribution 745
Table VI Percentage Points fα, , v v 1 2 of the F
Distribution 746
Chart VII Operating Characteristic Curves 751
Table VIII Critical Values for the Sign Test 760
Table IX Critical Values for the Wilcoxon Signed-Rank
Test 760
Table X Critical Values for the Wilcoxon Rank-Sum
Test 761
Table XI Factors for Constructing Variables Control
Charts 762
Table XII Factors for Tolerance Intervals 762
Appendix B: Bibliography 765
Appendix C: Answers to Selected Exercises 769
Glossary 787
Index 803
Index of applications in examples and
exercises, continued 809
