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Engineering Statistics
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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