Applied Statistics and Probability for Engineers, 5th Edition

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