Applied Statistics and Probability for Engineers

Cover Page......Page 1
Title Page......Page 5
Copyright Page......Page 6
Preface......Page 8
Contents......Page 15
CHAPTER 1 The Role of Statistics in Engineering......Page 19
1-1 The Engineering Method and Statistical Thinking......Page 20
1-2.2 Retrospective Study......Page 23
1-2.4 Designed Experiments......Page 24
1-2.5 Observing Processes Over Time......Page 27
1-3 Mechanistic and Empirical Models......Page 30
1-4 Probability and Probability Models......Page 33
CHAPTER 2 Probability......Page 35
2-1.1 Random Experiments......Page 36
2-1.2 Sample Spaces......Page 37
2-1.3 Events......Page 40
2-1.4 Counting Techniques......Page 42
2-2 Interpretations and Axioms of Probability......Page 49
2-3 Addition Rules......Page 55
2-4 Conditional Probability......Page 59
2-5 Multiplication and Total Probability Rules......Page 65
2-6 Independence......Page 68
2-7 Bayes’ Theorem......Page 73
2-8 Random Variables......Page 75
CHAPTER 3 Discrete Random Variables and Probability Distributions......Page 84
3-1 Discrete Random Variables......Page 85
3-2 Probability Distributions and Probability Mass Functions......Page 86
3-3 Cumulative Distribution Functions......Page 89
3-4 Mean and Variance of a Discrete Random Variable......Page 92
3-5 Discrete Uniform Distribution......Page 95
3-6 Binomial Distribution......Page 97
3-7 Geometric and Negative Binomial Distributions......Page 104
3-8 Hypergeometric Distribution......Page 110
3-9 Poisson Distribution......Page 115
CHAPTER 4 Continuous Random Variables and Probability Distributions......Page 125
4-2 Probability Distributions and Probability Density Functions......Page 126
4-3 Cumulative Distribution Functions......Page 129
4-4 Mean and Variance of a Continuous Random Variable......Page 132
4-5 Continuous Uniform Distribution......Page 134
4-6 Normal Distribution......Page 136
4-7 Normal Approximation to the Binomial and Poisson Distributions......Page 145
4-8 Exponential Distribution......Page 150
4-9 Erlang and Gamma Distributions......Page 156
4-10 Weibull Distribution......Page 159
4-11 Lognormal Distribution......Page 162
4-12 Beta Distribution......Page 164
CHAPTER 5 Joint Probability Distributions......Page 170
5-1.1 Joint Probability Distributions......Page 171
5-1.2 Marginal Probability Distributions......Page 174
5-1.3 Conditional Probability Distributions......Page 176
5-1.4 Independence......Page 179
5-1.5 More Than Two Random Variables......Page 181
5-2 Covariance and Correlation......Page 188
5-3.1 Multinomial Probability Distribution......Page 194
5-3.2 Bivariate Normal Distribution......Page 195
5-4 Linear Functions of Random Variables......Page 199
5-5 General Functions of Random Variables......Page 203
CHAPTER 6 Descriptive Statistics......Page 209
6-1 Numerical Summaries of Data......Page 210
6-2 Stem-and-Leaf Diagrams......Page 215
6-3 Frequency Distributions and Histograms......Page 221
6-4 Box Plots......Page 226
6-5 Time Sequence Plots......Page 228
6-6 Probability Plots......Page 232
CHAPTER 7 Sampling Distributions and Point Estimation of Parameters......Page 241
7-1 Point Estimation......Page 242
7-2 Sampling Distributions and the Central Limit Theorem......Page 243
7-3.1 Unbiased Estimators......Page 249
7-3.2 Variance of a Point Estimator......Page 250
7-3.3 Standard Error: Reporting a Point Estimate......Page 251
7-3.4 Mean Squared Error of an Estimator......Page 252
7-4.1 Method of Moments......Page 255
7-4.2 Method of Maximum Likelihood......Page 257
7-4.3 Bayesian Estimation of Parameters......Page 262
CHAPTER 8 Statistical Intervals for a Single Sample......Page 269
8-1.1 Development of the Confidence Interval and Its Basic Properties......Page 271
8-1.2 Choice of Sample Size......Page 274
8-1.3 One-sided Confidence Bounds......Page 275
8-1.5 Large-Sample Confidence Interval for μ......Page 276
8-2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown......Page 279
8-2.1 t Distribution......Page 280
8-2.2 t Confidence Interval on μ......Page 281
8-3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution......Page 284
8-4 Large-Sample Confidence Interval for a Population Proportion......Page 288
8-5 Guidelines for Constructing Confidence Intervals......Page 291
8-6.1 Prediction Interval for a Future Observation......Page 292
8-6.2 Tolerance Interval for a Normal Distribution......Page 294
CHAPTER 9 Tests of Hypotheses for a Single Sample......Page 301
9-1.1 Statistical Hypotheses......Page 302
9-1.2 Tests of Statistical Hypotheses......Page 304
9-1.3 One-Sided and Two-Sided Hypotheses......Page 310
9-1.4 P-Values in Hypothesis Tests......Page 312
9-1.5 Connection between Hypothesis Tests and Confidence Intervals......Page 313
9-1.6 General Procedure for Hypothesis Tests......Page 314
9-2.1 Hypothesis Tests on the Mean......Page 317
9-2.2 Type II Error and Choice of Sample Size......Page 321
9-2.3 Large-Sample Test......Page 325
9-3.1 Hypothesis Tests on the Mean......Page 328
9-3.2 Type II Error and Choice of Sample Size......Page 332
9-4.1 Hypothesis Tests on the Variance......Page 337
9-4.2 Type II Error and Choice of Sample Size......Page 340
9-5 Tests on a Population Proportion......Page 341
9-5.1 Large-Sample Tests on a Proportion......Page 342
9-5.2 Type II Error and Choice of Sample Size......Page 344
9-6 Summary Table of Inference Procedures for a Single Sample......Page 347
9-7 Testing for Goodness of Fit......Page 348
9-8 Contingency Table Tests......Page 351
9-9.1 The Sign Test......Page 355
9-9.2 The Wilcoxon Signed-Rank Test......Page 360
9-9.3 Comparison to the t-Test......Page 362
CHAPTER 10 Statistical Inference for Two Samples......Page 369
10-1 Inference on the Difference in Means of Two Normal Distributions, Variances Known......Page 370
10-1.1 Hypothesis Tests on the Difference in Means, Variances Known......Page 372
10-1.2 Type II Error and Choice of Sample Size......Page 374
10-1.3 Confidence Interval on the Difference in Means, Variances Known......Page 375
10-2.1 Hypotheses Tests on the Difference in Means, Variances Unknown......Page 379
10-2.2 Type II Error and Choice of Sample Size......Page 385
10-2.3 Confidence Interval on the Difference in Means, Variances Unknown......Page 386
10-3.1 Description of the Wilcoxon Rank-Sum Test......Page 391
10-3.2 Large-Sample Approximation......Page 392
10-3.3 Comparison to the t-Test......Page 393
10-4 Paired t-Test......Page 394
10-5 Inference on the Variances of Two Normal Distributions......Page 400
10-5.1 F Distribution......Page 401
10-5.2 Hypothesis Tests on the Ratio of Two Variances......Page 402
10-5.4 Confidence Interval on the Ratio of Two Variances......Page 405
10-6.1 Large-Sample Tests on the Difference in Population Proportions......Page 407
10-6.2 Type II Error and Choice of Sample Size......Page 409
10-6.3 Confidence Interval on the Difference in Population Proportions......Page 410
10-7 Summary Table and Roadmap for Inference Procedures for Two Samples......Page 412
CHAPTER 11 Simple Linear Regression and Correlation......Page 419
11-1 Empirical Models......Page 420
11-2 Simple Linear Regression......Page 423
11-3 Properties of the Least Squares Estimators......Page 432
11-4.1 Use of t-Tests......Page 433
11-4.2 Analysis of Variance Approach to Test Significance of Regression......Page 435
11-5.2 Confidence Interval on the Mean Response......Page 439
11-6 Prediction of New Observations......Page 441
11-7.1 Residual Analysis......Page 444
11-7.2 Coefficient of Determination (R2)......Page 446
11-8 Correlation......Page 449
11-9 Regression on Transformed Variables......Page 455
11-10 Logistic Regression......Page 458
CHAPTER 12 Multiple Linear Regression......Page 467
12-1.1 Introduction......Page 468
12-1.2 Least Squares Estimation of the Parameters......Page 470
12-1.3 Matrix Approach to Multiple Linear Regression......Page 474
12-1.4 Properties of the Least Squares Estimators......Page 478
12-2.1 Test for Significance of Regression......Page 488
12-2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients......Page 490
12-3.1 Confidence Intervals on Individual Regression Coefficients......Page 497
12-3.2 Confidence Interval on the Mean Response......Page 498
12-4 Prediction of New Observations......Page 499
12-5.1 Residual Analysis......Page 502
12-5.2 Influential Observations......Page 505
12-6.1 Polynomial Regression Models......Page 508
12-6.2 Categorical Regressors and Indicator Variables......Page 510
12-6.3 Selection of Variables and Model Building......Page 512
12-6.4 Multicollinearity......Page 520
CHAPTER 13 Design and Analysis of Single-Factor Experiments: The Analysis of Variance......Page 531
13-1 Designing Engineering Experiments......Page 532
13-2.1 Example: Tensile Strength......Page 533
13-2.2 Analysis of Variance......Page 535
13-2.3 Multiple Comparisons Following the ANOVA......Page 542
13-2.4 Residual Analysis and Model Checking......Page 544
13-2.5 Determining Sample Size......Page 545
13-3.1 Fixed Versus Random Factors......Page 551
13-3.2 ANOVA and Variance Components......Page 552
13-4.1 Design and Statistical Analysis......Page 556
13-4.2 Multiple Comparisons......Page 560
13-4.3 Residual Analysis and Model Checking......Page 562
CHAPTER 14 Design of Experiments with Several Factors......Page 569
14-1 Introduction......Page 570
14-2 Factorial Experiments......Page 573
14-3 Two-Factor Factorial Experiments......Page 576
14-3.1 Statistical Analysis of the Fixed-Effects Model......Page 577
14-3.2 Model Adequacy Checking......Page 582
14-3.3 One Observation per Cell......Page 584
14-4 General Factorial Experiments......Page 586
14-5.1 22 Design......Page 589
14-5.2 2k Design for k ≥ 3 Factors......Page 595
14-5.3 Single Replicate of the 2k Design......Page 602
14-5.4 Addition of Center Points to a 2k Design......Page 606
14-6 Blocking and Confounding in the 2k Design......Page 613
14-7.1 One-Half Fraction of the 2k Design......Page 620
14-7.2 Smaller Fractions: The 2k-p Fractional Factorial......Page 626
14-8 Response Surface Methods and Designs......Page 637
CHAPTER 15 Statistical Quality Control......Page 655
15-1 Quality Improvement and Statistics......Page 656
15-1.1 Statistical Quality Control......Page 657
15-2.1 Basic Principles......Page 658
15-2.2 Design of a Control Chart......Page 662
15-2.3 Rational Subgroups......Page 664
15-2.4 Analysis of Patterns on Control Charts......Page 665
15-3 X and R or S Control Charts......Page 667
15-4 Control Charts for Individual Measurements......Page 676
15-5 Process Capability......Page 680
15-6.1 P Chart (Control Chart for Proportions)......Page 686
15-6.2 U Chart (Control Chart for Defects per Unit)......Page 688
15-7 Control Chart Performance......Page 691
15-8.1 Cumulative Sum Control Chart......Page 694
15-8.2 Exponentially Weighted Moving Average Control Chart......Page 700
15-9 Other SPC Problem-Solving Tools......Page 706
15-10 Implementing SPC......Page 708
APPENDICES......Page 720
APPENDIX A: Statistical Tables and Charts......Page 721
Table I Summary of Common Probability Distributions......Page 722
Table II Cumulative Binomial Probabilities P(X ≤ x)......Page 723
Table III Cumulative Standard Normal Distribution......Page 726
Table IV Percentage Points X2α,ν of the Chi-Squared Distribution......Page 728
Table V Percentage Points tα,ν of the t distribution......Page 729
Table VI Percentage Points fα,v1,v2 of the F distribution......Page 730
Chart VII Operating Characteristic Curves......Page 735
Table IX Critical Values for the Wilcoxon Signed-Rank Test......Page 744
Table X Critical Values for the Wilcoxon Rank-Sum Test......Page 745
Table XI Factors for Constructing Variables Control Charts......Page 746
Table XII Factors for Tolerance Intervals......Page 747
APPENDIX B: Answers to Selected Exercises......Page 749
APPENDIX C: Bibliography......Page 767
GLOSSARY......Page 769
INDEX......Page 780
Index of Applications in Examples and Exercises......Page 790