Chapter 1 The Role of Statistics in Engineering 1

1-1 The Engineering Method and Statistical Thinking 2

1-2 Collecting Engineering Data 6

1-2.1 Retrospective Study 7

1-2.2 Observational Study 8

1-2.3 Designed Experiments 9

1-2.4 Random Samples 12

1-3 Mechanistic and Empirical Models 15

1-4 Observing Processes Over Time 17

Chapter 2 Data Summary and Presentation 23

2-1 Data Summary and Display 24

2-2 Stem-and-Leaf Diagram 29

2-3 Histograms 34

2-4 Box Plot 39

2-5 Time Series Plots 41

2-6 Multivariate Data 46

Chapter 3 Random Variables and Probability Distributions 57

3-1 Introduction 58

3-2 Random Variables 60

3-3 Probability 62

3-4 Continuous Random Variables 66

3-4.1 Probability Density Function 66

3-4.2 Cumulative Distribution Function 68

3-4.3 Mean and Variance 70

3-5 Important Continuous Distributions 74

3-5.1 Normal Distribution 74

3-5.2 Lognormal Distribution 84

3-5.3 Gamma Distribution 86

3-5.4 Weibull Distribution 86

3-5.5 Beta Distribution 88

3-6 Probability Plots 92

3-6.1 Normal Probability Plots 92

3-6.2 Other Probability Plots 94

3-7 Discrete Random Variables 97

3-7.1 Probability Mass Function 97

3-7.2 Cumulative Distribution Function 98

3-7.3 Mean and Variance 99

3-8 Binomial Distribution 102

3-9 Poisson Process 109

3-9.1 Poisson Distribution 109

3-9.2 Exponential Distribution 113

3-10 Normal Approximation to the Binomial and Poisson Distributions 119

3-11 More than One Random Variable and Independence 123

3-11.1 Joint Distributions 123

3-11.2 Independence 124

3-12 Functions of Random Variables 129

3-12.1 Linear Functions of Independent Random Variables 130

3-12.2 Linear Functions of Random Variables That are Not Independent 131

3-12.3 Nonlinear Functions of Independent Random Variables 133

3-13 Random Samples, Statistics, and the Central Limit Theorem 136

Chapter 4 Decision Making for a Single Sample 148

4-1 Statistical Inference 149

4-2 Point Estimation 150

4-3 Hypothesis Testing 156

4-3.1 Statistical Hypotheses 156

4-3.2 Testing Statistical Hypotheses 158

4-3.3 P-Values in Hypothesis Testing 164

4-3.4 One-Sided and Two-Sided Hypotheses 166

4-3.5 General Procedure for Hypothesis Testing 167

4-4 Inference on the Mean of a Population, Variance Known 169

4-4.1 Hypothesis Testing on the Mean 169

4-4.2 Type II Error and Choice of Sample Size 173

4-4.3 Large-Sample Test 177

4-4.4 Some Practical Comments on Hypothesis Testing 177

4-4.5 Confidence Interval on the Mean 178

4-4.6 General Method for Deriving a Confidence Interval 184

4-5 Inference on the Mean of a Population, Variance Unknown 186

4-5.1 Hypothesis Testing on the Mean 187

4-5.2 Type II Error and Choice of Sample Size 193

4-5.3 Confidence Interval on the Mean 195

4-6 Inference on the Variance of a Normal Population 199

4-6.1 Hypothesis Testing on the Variance of a Normal Population 199

4-6.2 Confidence Interval on the Variance of a Normal Population 203

4-7 Inference on a Population Proportion 205

4-7.1 Hypothesis Testing on a Binomial Proportion 205

4-7.2 Type II Error and Choice of Sample Size 208

4-7.3 Confidence Interval on a Binomial Proportion 210

4-8 Other Interval Estimates for a Single Sample 216

4-8.1 Prediction Interval 216

4-8.2 Tolerance Intervals for a Normal Distribution 217

4-9 Summary Tables of Inference Procedures for a Single Sample 219

4-10 Testing for Goodness of Fit 219

Chapter 5 Decision Making for Two Samples 230

5-1 Introduction 231

5-2 Inference on the Means of Two Populations, Variances Known 232

5-2.1 Hypothesis Testing on the Difference in Means, Variances Known 233

5-2.2 Type II Error and Choice of Sample Size 234

5-2.3 Confidence Interval on the Difference in Means, Variances Known 235

5-3 Inference on the Means of Two Populations, Variances Unknown 239

5-3.1 Hypothesis Testing on the Difference in Means 239

5-3.2 Type II Error and Choice of Sample Size 246

5-3.3 Confidence Interval on the Difference in Means 247

5-4 The Paired t-Test 252

5-5 Inference on the Ratio of Variances of Two Normal Populations 259

5-5.1 Hypothesis Testing on the Ratio of Two Variances 259

5-5.2 Confidence Interval on the Ratio of Two Variances 263

5-6 Inference on Two Population Proportions 265

5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions 265

5-6.2 Type II Error and Choice of Sample Size 268

5-6.3 Confidence Interval on the Difference in Binomial Proportions 269

5-7 Summary Tables for Inference Procedures for Two Samples 271

5-8 What if We Have More than Two Samples? 272

5-8.1 Completely Randomized Experiment and Analysis of Variance 272

5-8.2 Randomized Complete Block Experiment 281

Chapter 6 Building Empirical Models 298

6-1 Introduction to Empirical Models 299

6-2 Simple Linear Regression 304

6-2.1 Least Squares Estimation 304

6-2.2 Testing Hypotheses in Simple Linear Regression 312

6-2.3 Confidence Intervals in Simple Linear Regression 315

6-2.4 Prediction of a Future Observation 318

6-2.5 Checking Model Adequacy 319

6-2.6 Correlation and Regression 322

6-3 Multiple Regression 326

6-3.1 Estimation of Parameters in Multiple Regression 326

6-3.2 Inferences in Multiple Regression 331

6-3.3 Checking Model Adequacy 336

6-4 Other Aspects of Regression 344

6-4.1 Polynomial Models 344

6-4.2 Categorical Regressors 346

6-4.3 Variable Selection Techniques 348

Chapter 7 Design of Engineering Experiments 360

7-1 The Strategy of Experimentation 361

7-2 Factorial Experiments 362

7-3 2^k Factorial Design 365

7-3.1 2² Design 366

7-3.2 Statistical Analysis 368

7-3.3 Residual Analysis and Model Checking 374

7-3.4 2^k Design for k ¿ 3 Factors 376

7-3.5 Single Replicate of a 2^k Design 382

7-4 Center Points and Blocking in 2^k Designs 390

7-4.1 Addition of Center Points 390

7-4.2 Blocking and Confounding 393

7-5 Fractional Replication of a 2^k Design 398

7-5.1 One-Half Fraction of a 2^k Design 398

7-5.2 Smaller Fractions: 2^k-pFractional Factorial Designs 404

7-6 Response Surface Methods and Designs 414

7-6.1 Method of Steepest Ascent 416

7-6.2 Analysis of a Second-Order Response Surface 418

7-7 Factorial Experiments With More Than Two Levels 424

Chapter 8 Statistical Process Control 438

8-1 Quality Improvement and Statistical Process Control 439

8-2 Introduction to Control Charts 440

8-2.1 Basic Principles 440

8-2.2 Design of a Control Chart 444

8-2.3 Rational Subgroups 446

8-2.4 Analysis of Patterns on Control Charts 447

8-3 X¿ and R Control Charts 449

8-4 Control Charts For Individual Measurements 456

8-5 Process Capability 461

8-6 Attribute Control Charts 465

8-6.1 P Chart (Control Chart for Proportions) and nP Chart 465

8-6.2 U Chart (Control Chart for Average Number of Defects per Unit) and C Chart 467

8-7 Control Chart Performance 470

8-8 Measurement Systems Capability 473

Appendices 483

Appendix A Statistical Tables and Charts 485

Appendix B Bibliography 500

Appendix C* Answers to Selected Exercises 502

Index 511

Engineering Statistics, SI Version