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Copyright, ii
Preface, xiii
1. Collection and Analysis of Information, 1
1.1. Introduction, 1
1.1-1. Data Collection, 1
1.1-2. Types of Data, 3
1.1-3. The Study of Variability, 4
1.1-4. Distributions, 7
1.1-5. Importance of Variability (or Lack Thereof) for Quality and Productivity Improvement, 9
Exercises, 11
1.2. Measurements Collected over Time, 12
1.2-1. Time-Sequence Plots, 12
1.2-2. Control Charts: A Special Case of Time-Sequence Plots, 15
Exercises, 17
1.3. Data Display and Summary, 18
1.3-1. Summary and Display of Measurement Data, 18
1.3-2. Measures of Location, 22
1.3-3. Measures of Variation, 25
1.3-4. Exploratory Data Analysis: Stem-and-Leaf Displays and Box-and-Whisker Plots, 28
1.3-5. Analysis of Categorical Data, 32
Exercises, 36
1.4. Comparisons of Samples: The Importance of Stratification, 44
1.4-1. Comparing Two Types of Wires, 44
1.4-2. Comparing Lead Concentrations from Two Different Years, 45
1.4-3. Number of Flaws for Three Different Products, 48
1.4-4. Effects of Wind Direction on the Water Levels of Lake Neusiedl, 48
Exercises, 51
1.5. Graphical Techniques, Correlation, and an Introduction to Least Squares, 53
1.5-1. The Challenger Disaster, 53
1.5-2. The Sample Correlation Coefficient as a Measure of Association in a Scatter Plot, 55
1.5-3. Introduction to Least Squares, 59
Exercises, 61
1.6. The Importance of Experimentation, 65
1.6-1. Design of Experiments, 66
1.6-2. Design of Experiments with Several Factors and the Determination of Optimum Conditions, 70
Exercises, 72
1.7. Available Statistical Computer Software and the Visualization of Data, 73
1.7-1. Computer Software, 73
1.7-2. The Visualization of Data, 75
Exercises, 76
Chapter 1 Additional Remarks, 77
Projects, 78
2. Probability Models and Discrete Distributions, 87
2.1. Probability, 87
2.1-1. The Laws of Probability, 89
Exercises, 95
2.2. Conditional Probability and Independence, 96
2.2-1. Conditional Probability, 96
2.2-2. Independence, 98
2.2-3. Bayes’ Theorem, 100
Exercises, 102
2.3. Random Variables and Expectations, 106
2.3-1. Random Variables and Their Distributions, 106
2.3-2. Expectations of Random Variables, 109
Exercises, 112
2.4. The Binomial and Related Distributions, 114
2.4-1. Bernoulli Trials, 114
2.4-2. The Binomial Distribution, 115
2.4-3. The Negative Binomial Distribution, 119
2.4-4. The Hypergeometric Distribution, 119
Exercises, 120
2.5. Poisson Distribution and Poisson Process, 123
2.5-1. The Poisson Distribution, 123
2.5-2. The Poisson Process, 125
Exercises, 127
2.6. Multivariate Distributions, 129
2.6-1. Joint, Marginal, and Conditional Distributions, 129
2.6-2. Independence and Dependence of Random Variables, 133
2.6-3. Expectations of Functions of Several Random Variables, 134
2.6-4. Means and Variances of Linear Combinations of Random Variables, 138
Exercises, 139
2.7. The Estimation of Parameters from Random Samples, 142
2.7-1. Maximum Likelihood Estimation, 142
2.7-2. Examples, 143
2.7-3. Properties of Estimators, 145
Exercises, 147
Chapter 2 Additional Remarks, 148
Projects, 150
3. Continuous Probability Models, 153
3.1. Continuous Random Variables, 153
3.1-1. Empirical Distributions, 153
3.1-2. Distributions of Continuous Random Variables, 156
Exercises, 161
3.2. The Normal Distribution, 163
Exercises, 168
3.3. Other Useful Distributions, 170
3.3-1. Weibull Distribution, 171
3.3-2. Gompertz Distribution, 172
3.3-3. Extreme Value Distribution, 174
3.3-4. Gamma Distribution, 174
3.3-5. Chi-Square Distribution, 175
3.3-6. Lognormal Distribution, 175
Exercises, 179
3.4. Simulation: Generating Random Variables, 181
3.4-1. Motivation, 181
3.4-2. Generating Discrete Random Variables, 182
3.4-3. Generating Continuous Random Variables, 184
Exercises, 185
3.5. Distributions of Two or More Continuous Random Variables, 187
3.5-1. Joint, Marginal, and Conditional Distributions, and Mathematical Expectations, 187
3.5-2. Propagation of Errors, 188
Exercises, 191
3.6. Fitting and Checking Models, 194
3.6-1. Estimation of Parameters, 194
3.6-2. Checking for Normality, 196
3.6-3. Checking Other Models through Quantile–Quantile Plots, 200
Exercises, 204
3.7. Introduction to Reliability, 208
Exercises, 211
Chapter 3 Additional Remarks, 212
Projects, 214
4. Statistical Inference: Sampling Distributions, Confidence Intervals, and Tests of Hypotheses, 217
4.1. Sampling Distributions, 217
4.1-1. Introduction and Motivation, 217
4.1-2. Distribution of the Sample Mean X, 219
4.1-3. The Central Limit Theorem, 221
4.1-4. Normal Approximation of the Binomial Distribution, 223
Exercises, 225
4.2. Confidence Intervals for Means, 226
4.2-1. Determination of the Sample Size, 229
4.2-2. Confidence Intervals for μ_1 – μ_2, 230
Exercises, 231
4.3. Inferences from Small Samples and with Unknown Variances, 232
4.3-1. Tolerance Limits, 236
4.3-2. Confidence Intervals for μ_1 – μ_2, 239
Exercises, 240
4.4. Other Confidence Intervals, 242
4.4-1. Confidence Intervals for Variances, 242
4.4-2. Confidence Intervals for Proportions, 245
Exercises, 247
4.5. Tests of Characteristics of a Single Distribution, 248
4.5-1. Introduction, 248
4.5-2. Possible Errors and Operating Characteristic Curves, 250
4.5-3. Tests of Hypotheses When the Sample Size Can Be Selected, 252
4.5-4. Tests of Hypotheses When the Sample Size Is Fixed, 254
Exercises, 260
4.6. Tests of Characteristics of Two Distributions, 262
4.6-1. Comparing Two Independent Samples, 263
4.6-2. Paired-Sample t-Test, 265
4.6-3. Test of p_1 = p_2, 268
4.6-4. Test of {σ_1}^2 = {σ_2}^2, 269
Exercises, 270
4.7. Certain Chi-Square Tests, 272
4.7-1. Testing Hypotheses about Parameters in a Multinomial Distribution, 273
4.7-2. Contingency Tables and Tests of Independence, 276
4.7-3. Goodness-of-Fit Tests, 278
Exercises, 279
Chapter 4 Additional Remarks, 281
Projects, 283
5. Statistical Process Control, 293
5.1. Shewhart Control Charts, 293
5.1-1. x-Charts and R-charts, 294
5.1-2. p-Charts and c-Charts, 298
5.1-3. Other Control Charts, 302
Exercises, 302
5.2. Process Capability Indices, 305
5.2-1. Introduction, 305
5.2-2. Process Capability Indices, 308
5.2-3. Discussion of Process Capability Indices, 313
Exercises, 315
5.3. Acceptance Sampling, 316
Exercises, 321
5.4. Problem Solving, 322
5.4-1. Introduction, 322
5.4-2. Pareto Diagram, 323
5.4-3. Diagnosis of Causes of Defects, 325
5.4-4. Six Sigma Initiatives, 327
Exercises, 330
Chapter 5 Additional Remarks, 331
Projects, 333
6. Experiments with One Factor, 336
6.1. Completely Randomized One-Factor Experiments, 337
6.1-1. Analysis-of-Variance Table, 342
6.1-2. F-Test for Treatment Effects, 344
6.1-3. Graphical Comparison of k Samples, 345
Exercises, 345
6.2. Other Inferences in One-Factor Experiments, 349
6.2-1. Reference Distribution for Treatment Averages, 349
6.2-2. Confidence Intervals for a Particular Difference, 350
6.2-3. Tukey’s Multiple-Comparison Procedure, 351
6.2-4. Model Checking, 352
6.2-5. The Random-Effects Model, 352
6.2-6. Computer Software, 356
Exercises, 357
6.3. Randomized Complete Block Designs, 363
6.3-1. Estimation of Parameters and ANOVA, 365
6.3-2. Expected Mean Squares and Tests of Hypotheses, 367
6.3-3. Increased Efficiency by Blocking, 369
6.3-4. Follow-Up Tests, 369
6.3-5. Diagnostic Checking, 370
6.3-6. Computer Software, 372
Exercises, 372
6.4. Designs with Two Blocking Variables: Latin Squares, 375
6.4-1. Construction and Randomization of Latin Squares, 376
6.4-2. Analysis of Data from a Latin Square, 378
Exercises, 379
7. Experiments with Two or More Factors, 381
7.1. Two-Factor Factorial Designs, 381
7.1-1. Graphics in the Analysis of Two-Factor Experiments, 390
7.1-2. Special Case: n = 1, 391
7.1-3. Random Effects, 391
7.1-4. Computer Software, 392
Exercises, 392
7.2. Nested Factors and Hierarchical Designs, 395
Exercises, 400
7.3. General Factorial and 2^k Factorial Experiments, 404
7.3-1. 2^k Factorial Experiments, 405
7.3-2. Significance of Estimated Effects, 412
Exercises, 414
7.4. 2^{k–p} Fractional Factorial Experiments, 420
7.4-1. Half Fractions of 2^k Factorial Experiments, 421
7.4-2. Higher Fractions of 2^k Factorial Experiments, 424
7.4-3. Computer Software, 427
Exercises, 429
Chapters 6 and 7 Additional Remarks, 433
Chapters 6 and 7 Projects, 434
8. Regression Analysis, 437
8.1. The Simple Linear Regression Model, 438
8.1-1. Estimation of Parameters, 440
8.1-2. Residuals and Fitted Values, 443
8.1-3. Sampling Distribution of and β_0 β_1, 444
Exercises, 445
8.2. Inferences in the Regression Model, 448
8.2-1. Coefficient of Determination, 449
8.2-2. Analysis-of-Variance Table and F-Test, 450
8.2-3. Confidence Intervals and Tests of Hypotheses for Regression Coefficients, 452
Exercises, 455
8.3. The Adequacy of the Fitted Model, 457
8.3-1. Residual Checks, 457
8.3-2. Output from Computer Programs, 463
8.3-3. The Importance of Scatter Plots in Regression, 468
Exercises, 470
8.4. The Multiple Linear Regression Model, 477
8.4-1. Estimation of the Regression Coefficients, 478
8.4-2. Residuals, Fitted Values, and the Sum-of-Squares Decomposition, 480
8.4-3. Inference in the Multiple Linear Regression Model, 481
8.4-4. A Further Example: Formaldehyde Concentrations, 482
Exercises, 486
8.5. More on Multiple Regression, 492
8.5-1. Multicollinearity among the Explanatory Variables, 492
8.5-2. Another Example of Multiple Regression, 498
8.5-3. A Note on Computer Software, 504
8.5-4. Nonlinear Regression, 505
Exercises, 505
8.6. Response Surface Methods, 515
8.6-1. The “Change One Variable at a Time” Approach, 516
8.6-2. Method of Steepest Ascent, 517
8.6-3. Designs for Fitting Second-Order Models: The 3^k Factorial and the Central Composite Design, 519
8.6-4. Interpretation of the Second-Order Model, 521
8.6-5. An Illustration, 523
Exercises, 526
Chapter 8 Additional Remarks, 529
Projects, 530
Appendix A. References, 540
Appendix B. Answers to Selected Exercises, 546
Appendix C. Statistical Tables, 558
Appendix D. List of Files (Minitab and Text Files), 577
Index, 581

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