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 2k 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 2k Design for k 3 Factors 376
7-3.5 Single Replicate of a 2k Design 382
7-4 Center Points and Blocking in 2k Designs 390
7-4.1 Addition of Center Points 390
7-4.2 Blocking and Confounding 393
7-5 Fractional Replication of a 2k Design 398
7-5.1 One-Half Fraction of a 2k Design 398
7-5.2 Smaller Fractions: 2kp Fractional 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 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
*This section is available online at www.wiley.com/go/global/montgomery
