Engineering statistics

Cover......Page 1
Title Page......Page 7
Copyright......Page 8
About the Authors......Page 11
Preface......Page 12
Contents......Page 22
CHAPTER 1 The Role of Statistics in Engineering......Page 25
1-1 The Engineering Method and Statistical Thinking......Page 26
1-2 Collecting Engineering Data......Page 30
1-2.1 Retrospective Study......Page 31
1-2.2 Observational Study......Page 32
1-2.3 Designed Experiments......Page 33
1-2.4 Random Samples......Page 36
1-3 Mechanistic and Empirical Models......Page 39
1-4 Observing Processes Over Time......Page 41
CHAPTER 2 Data Summary and Presentation......Page 47
2-1 Data Summary and Display......Page 48
2-2 Stem-and-Leaf Diagram......Page 53
2-3 Histograms......Page 58
2-4 Box Plot......Page 63
2-5 Time Series Plots......Page 65
2-6 Multivariate Data......Page 70
CHAPTER 3 Random Variables and Probability Distributions......Page 81
3-1 Introduction......Page 82
3-2 Random Variables......Page 84
3-3 Probability......Page 86
3-4.1 Probability Density Function......Page 90
3-4.2 Cumulative Distribution Function......Page 92
3-4.3 Mean and Variance......Page 94
3-5.1 Normal Distribution......Page 98
3-5.2 Lognormal Distribution......Page 108
3-5.4 Weibull Distribution......Page 110
3-5.5 Beta Distribution......Page 112
3-6.1 Normal Probability Plots......Page 116
3-6.2 Other Probability Plots......Page 118
3-7.1 Probability Mass Function......Page 121
3-7.2 Cumulative Distribution Function......Page 122
3-7.3 Mean and Variance......Page 123
3-8 Binomial Distribution......Page 126
3-9.1 Poisson Distribution......Page 133
3-9.2 Exponential Distribution......Page 137
3-10 Normal Approximation to the Binomial and Poisson Distributions......Page 143
3-11.1 Joint Distributions......Page 147
3-11.2 Independence......Page 148
3-12 Functions of Random Variables......Page 153
3-12.1 Linear Functions of Independent Random Variables......Page 154
3-12.2 Linear Functions of Random Variables That Are Not Independent......Page 155
3-12.3 Nonlinear Functions of Independent Random Variables......Page 157
3-13 Random Samples, Statistics, and the Central Limit Theorem......Page 160
CHAPTER 4 Decision Making for a Single Sample......Page 172
4-1 Statistical Inference......Page 173
4-2 Point Estimation......Page 174
4-3.1 Statistical Hypotheses......Page 180
4-3.2 Testing Statistical Hypotheses......Page 182
4-3.3 P-Values in Hypothesis Testing......Page 188
4-3.4 One-Sided and Two-Sided Hypotheses......Page 190
4-3.5 General Procedure for Hypothesis Testing......Page 191
4-4.1 Hypothesis Testing on the Mean......Page 193
4-4.2 Type II Error and Choice of Sample Size......Page 197
4-4.4 Some Practical Comments on Hypothesis Testing......Page 201
4-4.5 Confidence Interval on the Mean......Page 202
4-4.6 General Method for Deriving a Confidence Interval......Page 208
4-5 Inference on the Mean of a Population, Variance Unknown......Page 210
4-5.1 Hypothesis Testing on the Mean......Page 211
4-5.2 Type II Error and Choice of Sample Size......Page 217
4-5.3 Confidence Interval on the Mean......Page 219
4-6.1 Hypothesis Testing on the Variance of a Normal Population......Page 223
4-6.2 Confidence Interval on the Variance of a Normal Population......Page 227
4-7.1 Hypothesis Testing on a Binomial Proportion......Page 229
4-7.2 Type II Error and Choice of Sample Size......Page 232
4-7.3 Confidence Interval on a Binomial Proportion......Page 234
4-8.1 Prediction Interval......Page 240
4-8.2 Tolerance Intervals for a Normal Distribution......Page 241
4-10 Testing for Goodness of Fit......Page 243
CHAPTER 5 Decision Making for Two Samples......Page 254
5-1 Introduction......Page 255
5-2 Inference on the Means of Two Populations, Variances Known......Page 256
5-2.1 Hypothesis Testing on the Difference in Means, Variances Known......Page 257
5-2.2 Type II Error and Choice of Sample Size......Page 258
5-2.3 Confidence Interval on the Difference in Means, Variances Known......Page 259
5-3.1 Hypothesis Testing on the Difference in Means......Page 263
5-3.2 Type II Error and Choice of Sample Size......Page 270
5-3.3 Confidence Interval on the Difference in Means......Page 271
5-4 The Paired t-Test......Page 276
5-5.1 Hypothesis Testing on the Ratio of Two Variances......Page 283
5-5.2 Confidence Interval on the Ratio of Two Variances......Page 287
5-6.1 Hypothesis Testing on the Equality of Two Binomial Proportions......Page 289
5-6.2 Type II Error and Choice of Sample Size......Page 292
5-6.3 Confidence Interval on the Difference in Binomial Proportions......Page 293
5-7 Summary Tables for Inference Procedures for Two Samples......Page 295
5-8.1 Completely Randomized Experiment and Analysis of Variance......Page 296
5-8.2 Randomized Complete Block Experiment......Page 305
CHAPTER 6 Building Empirical Models......Page 322
6-1 Introduction to Empirical Models......Page 323
6-2.1 Least Squares Estimation......Page 328
6-2.2 Testing Hypotheses in Simple Linear Regression......Page 336
6-2.3 Confidence Intervals in Simple Linear Regression......Page 339
6-2.4 Prediction of a Future Observation......Page 342
6-2.5 Checking Model Adequacy......Page 343
6-2.6 Correlation and Regression......Page 346
6-3.1 Estimation of Parameters in Multiple Regression......Page 350
6-3.2 Inferences in Multiple Regression......Page 355
6-3.3 Checking Model Adequacy......Page 360
6-4.1 Polynomial Models......Page 368
6-4.2 Categorical Regressors......Page 370
6-4.3 Variable Selection Techniques......Page 372
CHAPTER 7 Design of Engineering Experiments......Page 384
7-1 The Strategy of Experimentation......Page 385
7-2 Factorial Experiments......Page 386
7-3 2ᵏ Factorial Design......Page 389
7-3.1 2² Design......Page 390
7-3.2 Statistical Analysis......Page 392
7-3.3 Residual Analysis and Model Checking......Page 398
7-3.4 2ᵏ Design for k ≥ 3 Factors......Page 400
7-3.5 Single Replicate of a 2ᵏ Design......Page 406
7-4.1 Addition of Center Points......Page 414
7-4.2 Blocking and Confounding......Page 417
7-5.1 One-Half Fraction of a 2ᵏ Design......Page 422
7-5.2 Smaller Fractions: 2ᴷ⁻ᴾ Fractional Factorial Designs......Page 428
7-6 Response Surface Methods and Designs......Page 438
7-6.1 Method of Steepest Ascent......Page 440
7-6.2 Analysis of a Second-Order Response Surface......Page 442
7-7 Factorial Experiments With More Than Two Levels......Page 448
CHAPTER 8 Statistical Process Control......Page 462
8-1 Quality Improvement and Statistical Process Control......Page 463
8-2.1 Basic Principles......Page 464
8-2.2 Design of a Control Chart......Page 468
8-2.3 Rational Subgroups......Page 470
8-2.4 Analysis of Patterns on Control Charts......Page 471
8-3  X and R Control Charts......Page 473
8-4 Control Charts For Individual Measurements......Page 480
8-5 Process Capability......Page 485
8-6.1 P Chart (Control Chart for Proportions) and nP Chart......Page 489
8-6.2 U Chart (Control Chart for Average Number of Defects per Unit) and C Chart......Page 491
8-7 Control Chart Performance......Page 494
8-8 Measurement Systems Capability......Page 497
APPENDICES......Page 507
APPENDIX A: Statistical Tables and Charts......Page 509
APPENDIX B: Bibliography......Page 524
APPENDIX C: Answers to Selected Exercises......Page 526
INDEX......Page 535