Applied statistics and probability for engineers

Cover......Page 1
Title Page......Page 3
Copyright......Page 4
Preface......Page 6
Contents......Page 15
Chapter 1: The Role of Statistics in Engineering......Page 19
 1.1 The Engineering Method and Statistical Thinking......Page 20
  1.1.1 Variability......Page 21
  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 39
 2.2 Counting Techniques......Page 41
 2.3 Interpretations and Axioms of Probability......Page 44
 2.4 Unions of Events and Addition Rules......Page 47
 2.5 Conditional Probability......Page 49
 2.6 Intersections of Events and Multiplication and Total Probability Rules......Page 52
 2.7 Independence......Page 54
 2.8 Bayes' Theorem......Page 57
 2.9 Random Variables......Page 58
Chapter 3: Discrete Random Variables and Probability Distributions......Page 60
 3.1 Probability Distributions and Probability Mass Functions......Page 61
 3.2 Cumulative Distribution Functions......Page 63
 3.3 Mean and Variance of a Discrete Random Variable......Page 65
 3.4 Discrete Uniform Distribution......Page 67
 3.5 Binomial Distribution......Page 69
 3.6 Geometric and Negative Binomial Distributions......Page 73
 3.7 Hypergeometric Distribution......Page 77
 3.8 Poisson Distribution......Page 81
Chapter 4: Continuous Random Variables and Probability Distributions......Page 84
 4.1 Probability Distributions and Probability Density Functions......Page 85
 4.2 Cumulative Distribution Functions......Page 88
 4.3 Mean and Variance of a Continuous Random Variable......Page 89
 4.4 Continuous Uniform Distribution......Page 90
 4.5 Normal Distribution......Page 91
 4.6 Normal Approximation to the Binomial and Poisson Distributions......Page 97
 4.7 Exponential Distribution......Page 101
 4.8 Erlang and Gamma Distributions......Page 104
 4.9 Weibull Distribution......Page 107
 4.10 Lognormal Distribution......Page 108
 4.11 Beta Distribution......Page 110
Chapter 5: Joint Probability Distributions......Page 113
 5.1 Joint Probability Distributions for Two Random Variables......Page 114
 5.2 Conditional Probability Distributions and Independence......Page 120
 5.3 Joint Probability Distributions for More Than Two Random Variables......Page 125
 5.4 Covariance and Correlation......Page 128
  5.5.1 Multinomial Probability Distribution......Page 131
  5.5.2 Bivariate Normal Distribution......Page 133
 5.6 Linear Functions of Random Variables......Page 135
 5.7 General Functions of Random Variables......Page 138
 5.8 Moment-Generating Functions......Page 139
Chapter 6: Descriptive Statistics......Page 144
 6.1 Numerical Summaries of Data......Page 145
 6.2 Stem-and-Leaf Diagrams......Page 149
 6.3 Frequency Distributions and Histograms......Page 153
 6.4 Box Plots......Page 157
 6.5 Time Sequence Plots......Page 158
 6.6 Scatter Diagrams......Page 160
 6.7 Probability Plots......Page 162
Chapter 7: Point Estimation of Parameters and Sampling Distributions......Page 166
 7.1 Point Estimation......Page 167
 7.2 Sampling Distributions and the Central Limit Theorem......Page 168
  7.3.1 Unbiased Estimators......Page 174
  7.3.2 Variance of a Point Estimator......Page 175
  7.3.3 Standard Error: Reporting a Point Estimate......Page 176
  7.3.4 Bootstrap Standard Error......Page 177
  7.3.5 Mean Squared Error of an Estimator......Page 178
 7.4 Methods of Point Estimation......Page 179
  7.4.1 Method of Moments......Page 180
  7.4.2 Method of Maximum Likelihood......Page 181
  7.4.3 Bayesian Estimation of Parameters......Page 185
Chapter 8: Statistical Intervals for a Single Sample......Page 188
  8.1.1 Development of the Confidence Interval and Its Basic Properties......Page 190
  8.1.2 Choice of Sample Size......Page 193
  8.1.4 General Method to Derive a Confidence Interval......Page 194
  8.1.5 Large-Sample Confidence Interval for μ......Page 195
 8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown......Page 197
  8.2.1 t Distribution......Page 198
  8.2.2 Confidence Interval on μ......Page 199
 8.3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution......Page 200
 8.4 Large-Sample Confidence Interval for a Population Proportion......Page 203
 8.5 Guidelines for Constructing Confidence Intervals......Page 206
  8.7.1 Prediction Interval for a Future Observation......Page 207
  8.7.2 Tolerance Interval for a Normal Distribution......Page 209
Chapter 9: Tests of Hypotheses for a Single Sample......Page 211
  9.1.1 Statistical Hypotheses......Page 212
  9.1.2 Tests of Statistical Hypotheses......Page 214
  9.1.3 One-Sided and Two-Sided Hypotheses......Page 220
  9.1.4 P-Values in Hypothesis Tests......Page 221
  9.1.6 General Procedure for Hypothesis Tests......Page 224
  9.2.1 Hypothesis Tests on the Mean......Page 226
  9.2.2 Type II Error and Choice of Sample Size......Page 229
  9.3.1 Hypothesis Tests on the Mean......Page 233
  9.3.2 Type II Error and Choice of Sample Size......Page 238
  9.4.1 Hypothesis Tests on the Variance......Page 240
  9.4.2 Type II Error and Choice of Sample Size......Page 242
  9.5.1 Large-Sample Tests on a Proportion......Page 243
  9.5.2 Type II Error and Choice of Sample Size......Page 245
 9.7 Testing for Goodness of Fit......Page 247
 9.8 Contingency Table Tests......Page 250
 9.9 Nonparametric Procedures......Page 252
  9.9.1 The Sign Test......Page 253
  9.9.2 The Wilcoxon Signed-Rank Test......Page 257
 9.10 Equivalence Testing......Page 258
 9.11 Combining P-Values......Page 260
Chapter 10: Statistical Inference for Two Samples......Page 262
 10.1 Inference on the Difference in Means of Two Normal Distributions, Variances Known......Page 263
  10.1.1 Hypothesis Tests on the Difference in Means, Variances Known......Page 265
  10.1.2 Type II Error and Choice of Sample Size......Page 267
  10.1.3 Confidence Interval on the Difference in Means, Variances Known......Page 269
  10.2.1 Hypotheses Tests on the Difference in Means, Variances Unknown......Page 271
  10.2.2 Type II Error and Choice of Sample Size......Page 277
  10.2.3 Confidence Interval on the Difference in Means, Variances Unknown......Page 278
 10.3 A Nonparametric Test for the Difference in Two Means......Page 279
  10.3.1 Description of the Wilcoxon Rank-Sum Test......Page 280
  10.3.2 Large-Sample Approximation......Page 281
 10.4 Paired t-Test......Page 282
  10.5.1 F Distribution......Page 286
  10.5.2 Hypothesis Tests on the Equity of Two Variances......Page 288
  10.5.3 Type II Error and Choice of Sample Size......Page 290
 10.6 Inference on Two Population Proportions......Page 291
  10.6.1 Large-Sample Tests on the Difference in Population Proportions......Page 292
  10.6.2 Type II Error and Choice of Sample Size......Page 294
  10.6.3 Confidence Interval on the Difference in Population Proportions......Page 295
 10.7 Summary Table and Road Map for Inference Procedures for Two Samples......Page 296
Chapter 11: Simple Linear Regression and Correlation......Page 298
 11.1 Empirical Models......Page 299
 11.2 Simple Linear Regression......Page 302
 11.4 Hypothesis Tests in Simple Linear Regression......Page 306
  11.4.1 Use of t-Tests......Page 307
  11.4.2 Analysis of Variance Approach to Test Significance of Regression......Page 309
  11.5.1 Confidence Intervals on the Slope and Intercept......Page 310
  11.5.2 Confidence Interval on the Mean Response......Page 311
 11.6 Prediction of New Observations......Page 313
  11.7.1 Residual Analysis......Page 314
  11.7.2 Coefficient of Determination (R2)......Page 316
 11.8 Correlation......Page 317
 11.9 Regression on Transformed Variables......Page 321
 11.10 Logistic Regression......Page 323
Chapter 12: Multiple Linear Regression......Page 328
  12.1.1 Introduction......Page 329
  12.1.2 Least Squares Estimation of the Parameters......Page 332
  12.1.3 Matrix Approach to Multiple Linear Regression......Page 334
  12.1.4 Properties of the Least Squares Estimators......Page 339
  12.2.1 Test for Significance of Regression......Page 340
  12.2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients......Page 343
  12.3.1 Confidence Intervals on Individual Regression Coefficients......Page 347
  12.3.2 Confidence Interval on the Mean Response......Page 348
 12.4 Prediction of New Observations......Page 349
  12.5.1 Residual Analysis......Page 351
  12.5.2 Influential Observations......Page 353
  12.6.1 Polynomial Regression Models......Page 355
  12.6.2 Categorical Regressors and Indicator Variables......Page 357
  12.6.3 Selection of Variables and Model Building......Page 359
  12.6.4 Multicollinearity......Page 367
Chapter 13: Design and Analysis of Single-Factor Experiments: The Analysis of Variance......Page 369
 13.1 Designing Engineering Experiments......Page 370
  13.2.1 Example: Tensile Strength......Page 371
  13.2.2 Analysis of Variance......Page 372
  13.2.3 Multiple Comparisons Following the ANOVA......Page 377
  13.2.4 Residual Analysis and Model Checking......Page 379
  13.2.5 Determining Sample Size......Page 381
  13.3.2 ANOVA and Variance Components......Page 383
  13.4.1 Design and Statistical Analysis......Page 386
  13.4.2 Multiple Comparisons......Page 390
  13.4.3 Residual Analysis and Model Checking......Page 391
Chapter 14: Design of Experiments with Several Factors......Page 393
 14.1 Introduction......Page 394
 14.2 Factorial Experiments......Page 396
  14.3.1 Statistical Analysis......Page 400
  14.3.2 Model Adequacy Checking......Page 404
  14.3.3 One Observation per Cell......Page 405
 14.4 General Factorial Experiments......Page 406
  14.5.1 22 Design......Page 408
  14.5.2 2k Design for k ≥ 3 Factors......Page 414
 14.6 Single Replicate of the 2k Design......Page 420
 14.7 Addition of Center Points to a 2k Design......Page 423
 14.8 Blocking and Confounding in the 2k Design......Page 426
 14.9 One-Half Fraction of the 2k Design......Page 431
 14.10 Smaller Fractions: The 2k-p Fractional Factorial......Page 436
 14.11 Response Surface Methods and Designs......Page 443
Chapter 15: Statistical Quality Control......Page 452
 15.1 Quality Improvement and Statistics......Page 453
  15.2.1 Basic Principles......Page 454
  15.2.2 Design of a Control Chart......Page 458
  15.2.3 Rational Subgroups......Page 459
  15.2.4 Analysis of Patterns on Control Charts......Page 460
 15.3 X and R or S Control Charts......Page 462
 15.4 Control Charts for Individual Measurements......Page 468
 15.5 Process Capability......Page 470
  15.6.1 P Chart (Control Chart for Proportions)......Page 474
  15.6.2 U Chart (Control Chart for Defects per Unit)......Page 476
 15.7 Control Chart Performance......Page 478
  15.8.1 Exponentially Weighted Moving-Average Control Chart......Page 480
  15.8.2 Cumulative Sum Control Chart......Page 483
 15.9 Other SPC Problem-Solving Tools......Page 489
  15.10.1 Decision Models......Page 491
  15.10.2 Decision Criteria......Page 492
 15.11 Implementing SPC......Page 494
Appendix A: Statistical Tables and Charts......Page 501
 Table I Summary of Common Probability Distributions......Page 502
 Table II Cumulative Binomial Probabilities P(X ≤ x)......Page 503
 Table III Cumulative Standard Normal Distribution......Page 506
 Table IV Percentage Points χ2α,v of the Chi-Squared Distribution......Page 508
 Table V Percentage Points tα,v of the t Distribution......Page 509
 Table VI Percentage Points fα,v1,v2of the F Distribution......Page 510
 Chart VII Operating Characteristic Curves......Page 516
 Table IX Critical Values for the Wilcoxon Signed-Rank Test......Page 524
 Table X Critical Values for the Wilcoxon Rank-Sum Test......Page 525
 Table XI Factors for Constructing Variables Control Charts......Page 526
 Table XII Factors for Tolerance Intervals......Page 527
Appendix B: Bibliography......Page 529
Glossary......Page 531
Exercises......Page 541
Index......Page 689
EULA......Page 710