Modern Engineering Statistics

Preface xvii

1. Methods of Collecting and Presenting Data 1

1.1 Observational Data and Data from Designed Experiments 3

1.2 Populations and Samples 5

1.3 Variables 6

1.4 Methods of Displaying Small Data Sets 7

1.5 Methods of Displaying Large Data Sets 16

1.6 Outliers 22

1.7 Other Methods 22

1.8 Extremely Large Data Sets: Data Mining 23

1.9 Graphical Methods: Recommendations 23

1.10 Summary 24

References 24

Exercises 25

2. Measures of Location and Dispersion 45

2.1 Estimating Location Parameters 46

2.2 Estimating Dispersion Parameters 50

2.3 Estimating Parameters from Grouped Data 55

2.4 Estimates from a Boxplot 57

2.5 Computing Sample Statistics with MINITAB 58

2.6 Summary 58

Reference 58

Exercises 58

3. Probability and Common Probability Distributions 68

3.1 Probability: From the Ethereal to the Concrete 68

3.3 Common Discrete Distributions 76

3.4 Common Continuous Distributions 92

3.5 General Distribution Fitting 106

3.6 How to Select a Distribution 107

3.7 Summary 108

References 109

Exercises 109

4. Point Estimation 121

4.1 Point Estimators and Point Estimates 121

4.2 Desirable Properties of Point Estimators 121

4.3 Distributions of Sampling Statistics 125

4.4 Methods of Obtaining Estimators 128

4.5 Estimating σ_θ 132

4.6 Estimating Parameters Without Data 133

4.7 Summary 133

References 134

Exercises 134

5. Confidence Intervals and Hypothesis Tests—One Sample 140

5.1 Confidence Interval for μ: Normal Distribution σ Not Estimated from Sample Data 140

5.2 Confidence Interval for μ: Normal Distribution σ Estimated from Sample Data 146

5.3 Hypothesis Tests for μ: Using Z and t 147

5.4 Confidence Intervals and Hypothesis Tests for a Proportion 157

5.5 Confidence Intervals and Hypothesis Tests for σ² and σ 161

5.6 Confidence Intervals and Hypothesis Tests for the Poisson Mean 164

5.7 Confidence Intervals and Hypothesis Tests When Standard Error Expressions are Not Available 166

5.8 Type I and Type II Errors 168

5.9 Practical Significance and Narrow Intervals: The Role of n 172

5.10 Other Types of Confidence Intervals 173

5.11 Abstract of Main Procedures 174

5.12 Summary 175

Appendix: Derivation 176

References 176

Exercises 177

6. Confidence Intervals and Hypothesis Tests—Two Samples 189

6.1 Confidence Intervals and Hypothesis Tests for Means: Independent Samples 189

6.2 Confidence Intervals and Hypothesis Tests for Means: Dependent Samples 197

6.3 Confidence Intervals and Hypothesis Tests for Two Proportions 200

6.4 Confidence Intervals and Hypothesis Tests for Two Variances 202

6.5 Abstract of Procedures 204

6.6 Summary 205

References 205

Exercises 205

7. Tolerance Intervals and Prediction Intervals 214

7.1 Tolerance Intervals: Normality Assumed 215

7.2 Tolerance Intervals and Six Sigma 219

7.3 Distribution-Free Tolerance Intervals 219

7.4 Prediction Intervals 221

7.5 Choice Between Intervals 227

7.6 Summary 227

References 228

Exercises 229

8. Simple Linear Regression Correlation and Calibration 232

8.1 Introduction 232

8.2 Simple Linear Regression 232

8.3 Correlation 254

8.4 Miscellaneous Uses of Regression 256

8.5 Summary 264

References 264

Exercises 265

9. Multiple Regression 276

9.1 How Do We Start? 277

9.2 Interpreting Regression Coefficients 278

9.3 Example with Fixed Regressors 279

9.4 Example with Random Regressors 281

9.5 Example of Section 8.2.4 Extended 291

9.6 Selecting Regression Variables 293

9.7 Transformations 299

9.8 Indicator Variables 300

9.9 Regression Graphics 300

9.10 Logistic Regression and Nonlinear Regression Models 301

9.11 Regression with Matrix Algebra 302

9.12 Summary 302

References 303

Exercises 304

10. Mechanistic Models 314

10.1 Mechanistic Models 315

10.2 Empirical–Mechanistic Models 316

10.3 Additional Examples 324

10.4 Software 325

10.5 Summary 326

References 326

Exercises 327

11. Control Charts and Quality Improvement 330

11.1 Basic Control Chart Principles 330

11.2 Stages of Control Chart Usage 331

11.3 Assumptions and Methods of Determining Control Limits 334

11.4 Control Chart Properties 335

11.5 Types of Charts 336

11.6 Shewhart Charts for Controlling a Process Mean and Variability (Without Subgrouping) 336

11.7 Shewhart Charts for Controlling a Process Mean and Variability (With Subgrouping) 344

11.8 Important Use of Control Charts for Measurement Data 349

11.9 Shewhart Control Charts for Nonconformities and Nonconforming Units 349

11.10 Alternatives to Shewhart Charts 356

11.11 Finding Assignable Causes 359

11.12 Multivariate Charts 362

11.13 Case Study 362

11.14 Engineering Process Control 364

11.15 Process Capability 365

11.16 Improving Quality with Designed Experiments 366

11.17 Six Sigma 367

11.18 Acceptance Sampling 368

11.19 Measurement Error 368

11.20 Summary 368

References 369

Exercises 370

12. Design and Analysis of Experiments 382

12.1 Processes Must be in Statistical Control 383

12.2 One-Factor Experiments 384

12.3 One Treatment Factor and at Least One Blocking Factor 392

12.4 More Than One Factor 395

12.5 Factorial Designs 396

12.6 Crossed and Nested Designs 405

12.7 Fixed and Random Factors 406

12.8 ANOM for Factorial Designs 407

12.9 Fractional Factorials 409

12.10 Split-Plot Designs 413

12.11 Response Surface Designs 414

12.12 Raw Form Analysis Versus Coded Form Analysis 415

12.13 Supersaturated Designs 416

12.14 Hard-to-Change Factors 416

12.15 One-Factor-at-a-Time Designs 417

12.16 Multiple Responses 418

12.17 Taguchi Methods of Design 419

12.18 Multi-Vari Chart 420

12.19 Design of Experiments for Binary Data 420

12.20 Evolutionary Operation (EVOP) 421

12.21 Measurement Error 422

12.22 Analysis of Covariance 422

12.23 Summary of MINITAB and Design-Expert^® Capabilities for Design of Experiments 422

12.24 Training for Experimental Design Use 423

12.25 Summary 423

Appendix A Computing Formulas 424

Appendix B Relationship Between Effect Estimates and

Regression Coefficients 426

References 426

Exercises 428

13. Measurement System Appraisal 441

13.1 Terminology 442

13.2 Components of Measurement Variability 443

13.3 Graphical Methods 449

13.4 Bias and Calibration 449

13.5 Propagation of Error 454

13.6 Software 455

13.7 Summary 456

References 456

Exercises 457

14. Reliability Analysis and Life Testing 460

14.1 Basic Reliability Concepts 461

14.2 Nonrepairable and Repairable Populations 463

14.3 Accelerated Testing 463

14.4 Types of Reliability Data 466

14.5 Statistical Terms and Reliability Models 467

14.6 Reliability Engineering 473

14.7 Example 474

14.8 Improving Reliability with Designed Experiments 474

14.9 Confidence Intervals 477

14.10 Sample Size Determination 478

14.11 Reliability Growth and Demonstration Testing 479

14.12 Early Determination of Product Reliability 480

14.13 Software 480

14.14 Summary 481

References 481

Exercises 482

15. Analysis of Categorical Data 487

15.1 Contingency Tables 487

15.2 Design of Experiments: Categorical Response Variable 497

15.3 Goodness-of-Fit Tests 498

15.4 Summary 500

References 500

Exercises 501

16. Distribution-Free Procedures 507

16.1 Introduction 507

16.2 One-Sample Procedures 508

16.3 Two-Sample Procedures 512

16.4 Nonparametric Analysis of Variance 514

16.5 Exact Versus Approximate Tests 519

16.6 Nonparametric Regression 519

16.7 Nonparametric Prediction Intervals and Tolerance Intervals 521

16.8 Summary 521

References 521

Exercises 522

17. Tying It All Together 525

17.1 Review of Book 525

17.2 The Future 527

17.3 Engineering Applications of Statistical Methods 528

Reference 528

Exercises 528

Answers to Selected Excercises 533

Appendix: Statistical Tables 562

Table A Random Numbers 562

Table B Normal Distribution 564

Table C t-Distribution 566

Table D F-Distribution 567

Table E Factors for Calculating Two-Sided 99% Statistical Intervals for a Normal Population to Contain at Least 100p% of the Population 570

Table F Control Chart Constants 571

Author Index 573

Subject Index 579