Applied statistics and probability for engineers / Douglas C. Montgomery, Arizona State University, George C. Runger, Arizona State University.

Includes bibliographical references and index.

TABLE OF CONTENTS:

1 The Role of Statistics in Engineering, p.1 -- 1.1 The Engineering Method and Statistical Thinking, p.2 -- 1.1.1 Variability, p.3 -- 1.1.2 Populations and Samples, p.5 -- 1.2 Collecting Engineering Data, p.5 -- 1.2.1 Basic Principles, p.5 -- 1.2.2 Retrospective Study 5 -- 1.2.3 Observational Study, p.6 -- 1.2.4 Designed Experiments, p.6 -- 1.2.5 Observing Processes Over Time, p.9 -- 1.3 Mechanistic and Empirical Models, p.12 -- 1.4 Probability and Probability Models, p.15 -- 2 Probabilit, p.17 -- 2.1 Sample Spaces and Events, p.18 -- 2.1.1 Random Experiments, p.18 -- 2.1.2 Sample Spaces, p.19 -- 2.1.3 Events, p.21 -- 2.2 Counting Techniques, p.23 -- 2.3 Interpretations and Axioms of Probability, p.26 -- 2.4 Unions of Events and Addition Rules, p.29 -- 2.5 Conditional Probability, p.31 -- 2.6 Intersections of Events and Multiplication and Total Probability Rules, p.34 -- 2.7 Independence, p.36 -- 2.8 Bayes’ Theorem, p.39 -- 2.9 Random Variables, p.40 -- 3 Discrete Random Variables and Probability Distributions, p.42 -- 3.1 Probability Distributions and Probability Mass Functions, p.43 -- 3.2 Cumulative Distribution Functions, p.45 3.3 Mean and Variance of a Discrete Random Variable, p.47 3.4 Discrete Uniform Distribution, p.49 -- 3.5 Binomial Distribution, p.51 -- 3.6 Geometric and Negative Binomial Distributions, p.55 -- 3.7 Hypergeometric Distribution, p.59 -- 3.8 Poisson Distribution, p.63 -- 4 Continuous Random Variables and Probability Distributions, p.66 -- 4.1 Probability Distributions and Probability Density Functions, p.67 -- 4.2 Cumulative Distribution Functions, p.70 -- 4.3 Mean and Variance of a Continuous Random Variable, p.71 -- 4.4 Continuous Uniform Distribution, p.72 -- 4.5 Normal Distribution, p.73 -- 4.6 Normal Approximation to the Binomial and Poisson Distributions, p.79 -- 4.7 Exponential Distribution, p.83 -- 4.8 Erlang and Gamma Distributions, p.86 -- 4.9 Weibull Distribution, p.89 -- 4.10 Lognormal Distribution, p.90 -- 4.11 Beta Distribution, p.92 -- 5 Joint Probability Distributions, p.95 -- 5.1 Joint Probability Distributions for Two Random Variables, p.96 -- 5.2 Conditional Probability Distributions and Independence, p.102 -- 5.3 Joint Probability Distributions for More Than Two Random Variables, p.107 -- 5.4 Covariance and Correlation, p.110 -- 5.5 Common Joint Distributions, p.113 -- 5.5.1 Multinomial Probability Distribution, p.113 -- 5.5.2 Bivariate Normal Distribution, p.115 -- 5.6 Linear Functions of Random Variables, p.117 -- 5.7 General Functions of Random Variables, p.120 -- 5.8 Moment-Generating Functions, p.121 -- 6 Descriptive Statistics, p.126 -- 6.1 Numerical Summaries of Data, p.127 -- 6.2 Stem-and-Leaf Diagrams, p.131 -- 6.3 Frequency Distributions and Histograms, p.135 -- 6.4 Box Plots, p.139 -- 6.5 Time Sequence Plots, p.140 -- 6.6 Scatter Diagrams, p.142 -- 6.7 Probability Plots, p.144 -- 7 Point Estimation of Parameters and Sampling Distributions, p.148 -- 8.6 Bootstrap Confidence Interval, p.189 -- 8.7 Tolerance and Prediction Intervals, p.189 -- 8.7.1 Prediction Interval for a Future Observation, p.189 -- 8.7.2 Tolerance Interval for a Normal Distribution, p.191 -- 9 Tests of Hypotheses for a Single Sample, p.193 -- 7.1 Point Estimation, p.149 7.2 Sampling Distributions and the Central Limit Theorem, p.150 7.3 General Concepts of Point Estimation, p.156 7.3.1 Unbiased Estimators, p.156 7.3.2 Variance of a Point Estimator, p.157 -- 7.3.3 Standard Error: Reporting a Point Estimate, p.158 -- 7.3.4 Bootstrap Standard Error, p.159 -- 7.3.5 -- Mean Squared Error of an Estimator, p.160 -- 7.4 Methods of Point Estimation, p.161 -- 7.4.1 Method of Moments, p.162 -- 7.4.2 Method of Maximum Likelihood, p.163 -- 7.4.3 Bayesian Estimation of Parameters, p.167 -- 8 Statistical Intervals for a Single Sample, p.170 -- 8.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known, p.172 -- 8.1.1 Development of the Confidence Interval and Its Basic Properties, p.172 -- 8.1.2 Choice of Sample Size, p.175 -- 8.1.3 One-Sided Confidence Bounds, p.176 -- 8.1.4 General Method to Derive a Confidence Interval, p.176 -- 8.1.5 Large-Sample Confidence Interval for p, p.177 -- 8.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown, p.179 -- 8.2.1 t Distribution, p.180 -- 8.2.2 t Confidence Interval on p, p.181 -- 8.3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution, p.182 -- 8.4 Large-Sample Confidence Interval for a Population Proportion, p.185 -- 8.5 Guidelines for Constructing Confidence Intervals, p.188 -- 8.6 Bootstrap Confidence Interval, p.189 -- 8.7 Tolerance and Prediction Intervals, p.189 -- 8.7.1 Prediction Interval for a Future Observation, p.189 -- 8.7.2 Tolerance Interval for a Normal Distribution, p.191 -- 9 Tests of Hypotheses for a Single Sample, p.193 -- 9.1 Hypothesis Testing, p.194 -- 9.1.1 Statistical Hypotheses, p.194 -- 9.1.2 Tests of Statistical Hypotheses, p.196 -- 9.1.3 One-Sided and Two-Sided Hypotheses, p.202 -- 9.1.4 P-Values in Hypothesis Tests, p.203 -- 9.1.5 Connection between Hypothesis Tests and Confidence Intervals, p.206 -- 9.1.6 General Procedure for Hypothesis Tests, p.206 -- 9.2 Tests on the Mean of a Normal Distribution, Variance Known, p.208 -- 9.2.1 Hypothesis Tests on the Mean, p.208 -- 9.2.2 Type II Error and Choice of Sample Size, p.211 -- 9.2.3 Large-Sample Test, p.215 -- 9.3 Tests on the Mean of a Normal Distribution, Variance Unknown, p.215 -- 9.3.1 Hypothesis Tests on the Mean, p.215 -- 9.3.2 Type ll Error and Choice of Sample Size, p.220 -- 9.4 Tests on the Variance and Standard Deviation of a Normal Distribution, p.222 -- 9.4.1 Hypothesis Tests on the Variance, p.222 -- 9.4.2 Type II Error and Choice of Sample Size, p.224 -- 9.5 Tests on a Population Proportion, p.225 -- 9.5.1 Large-Sample Tests on a Proportion, p.225 -- 9.5.2 Type II Error and Choice of Sample Size, p.227 -- 9.6 Summary Table of Inference Procedures for a Single Sample, p.229 -- 9.7 Testing for Goodness of Fit, p.229 -- 9.8 Contingency Table Tests, p.232 -- 9.9 Nonparametric Procedures, p.234 -- 9.9.1 The Sign Test, p.235 -- 9.9.2 The Wilcoxon Signed-Rank Test, p.239 -- 9.9.3 Comparison to the t-Test, p.240 -- 9.10 Equivalence Testing, p.240 -- 9.11 Combining P-Values, p.242 -- 10 Statistical Inference for Two Samples, p.244 -- 10.1 Inference on the Difference in Means of Two Normal Distributions, Variances Known, p.245 -- 10.1.1 Hypothesis Tests on the Difference in Means, Variances Known, p.247 -- 10.1.2 Type II Error and Choice of Sample Size, p.249 -- 10.1.3 Confidence Interval on the Difference in Means, Variances Known, p.251 -- 10.2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown, p.253 -- 10.2.1 Hypotheses Tests on the Difference in Means, Variances Unknown, p.253 -- 10.2.2 Type II Error and Choice of Sample Size, p.259 -- 10.2.3 Confidence Interval on the Difference in Means, Variances Unknown, p.260 -- 10.3 A Nonparametric Test for the Difference in Two Means, p.261 -- 10.3.1 Description of the Wilcoxon Rank-Sum Test, p.262 -- 10.3.2 Large-Sample Approximation, p.263 -- 10.3.3 Comparison to the f-Test, p.264 -- 10.4 Paired t-Test, p.264 -- 10.5 Inference on the Variances of Two Normal Distributions, p.268 -- 10.5.1 F Distribution, p.268 -- 10.5.2 Hypothesis Tests on the Equity of Two Variances, p.270 -- 10.5.3 Type II Error and Choice of Sample Size, p.272 -- 10.5.4 Confidence Interval on the Ratio of Two Variances, p.273 -- 10.6 Inference on Two Population Proportions, p.273 -- 10.6.1 Large-Sample Tests on the Difference in Population Proportions, p.274 -- 10.6.2 Type II Error and Choice of Sample Size, p.276 -- 10.6.3 Confidence Interval on the Difference in Population Proportions, p.277 -- 10.7 Summary Table and Road Map for Inference Procedures for Two Samples, p.278 -- 11 Simple Linear Regression and Correlation, p.280 -- 11.1 Empirical Models, p.281 -- 11.2 Simple Linear Regression, p.284 -- 11.3 Properties of the Least Squares Estimators, p.288 -- 11.4 Hypothesis Tests in Simple Linear Regression, p.288 -- 11.4.1 Useoft-Tests, p.289 -- 11.4.2 Analysis of Variance Approach to Test Significance of Regression, p.291 -- 11.5 Confidence Intervals, p.292 -- 11.5.1 Confidence Intervals on the Slope and Intercept, p.292 -- 11.5.2 Confidence Interval on the Mean Response, p.293 -- 11.6 Prediction of New Observations, p.295 -- 11.7 Adequacy of the Regression Model, p.296 -- 11.7.1 Residual Analysis, p.296 -- 11.7.2 Coefficient of Determination [R2), p.298 -- 11.8 Correlation, p.299 -- 11.9 Regression on Transformed Variables, p.303 -- 11.10 Logistic Regression, p.305 -

12 Multiple Linear Regression, p.310 -- 12.1 Multiple Linear Regression Model, p.311 -- 12.1.1 Introduction, p.311 12.1.2 Least Squares Estimation of the Parameters, p.314 -- 12.1.3 Matrix Approach to Multiple Linear Regression, p.316 -- 12.1.4 Properties of the Least Squares Estimators, p.321 -- 12.2 Hypothesis Tests in Multiple Linear Regression, p.322 -- 12.2.1 Test for Significance of Regression, p.322 -- 12.2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients, p.325 -- 12.3 Confidence Intervals in Multiple Linear Regression, p.329 -- 12.3.1 Confidence Intervals on Individual Regression Coefficients, p.329 -- 12.3.2 Confidence Interval on the Mean Response, p.330 -- 12.4 Prediction of New Observations, p.331 -- 12.5 Model Adequacy Checking, p.333 -- 12.5.1 Residual Analysis, p.333 -- 12.5.2 Influential Observations, p.335 -- 12.6 Aspects of Multiple Regression Modeling, p.337 -- 12.6.1 Polynomial Regression Models, p.337 -- 12.6.2 Categorical Regressors and Indicator Variables, p.339 -- 12.6.3 Selection of Variables and Model Building, p.341 -- 12.6.4 Multicollinearity, p.349 -- 13 Design and Analysis of Single-Factor Experiments: The Analysis of Variance, p.351 -- 13.1 Designing Engineering Experiments, p.352 -- 13.2 Completely Randomized Single-Factor Experiment, p.353 -- 13.2.1 Example: Tensile Strength, p.353 -- 13.2.2 Analysis of Variance, p.354 -- 13.2.3 Multiple Comparisons Following theANOVA, p.359 -- 13.2.4 Residual Analysis and Model Checking, p.361 13.2.5 Determining Sample Size, p.363 -- 13.3 The Random-Effects Model, p.365 -- 13.3.1 Fixed Versus Random Factors, p.365 -- 13.3.2 ANOVA and Variance Components, p.365 -- 13.4 Randomized Complete Block Design, p.368 -- 13.4.1 Design and Statistical Analysis, p.368 -- 13.4.2 Multiple Comparisons, p.372 -- 13.4.3 Residual Analysis and Model Checking, p.373 -- 15.2.3 Rational Subgroups, p.441 -- 15.2.4 Analysis of Patterns on Control Charts, p.442 -- 15.3 X and/? or S Control Charts, p.444 -- 15.4 Control Charts for Individual Measurements, p.450 -- 15.5 Process Capability, p.452 -- 15.6 Attribute Control Charts, p.456 -- 15.6.1 P Chart (Control Chart for Proportions), p.456 -- 15.6.2 U Chart (Control Chart for Defects per Unit), p.458 -- 15.7 Control Chart Performance, p.460 -- 15.8 Time-Weighted Charts, p.462 -- 15.8.1 Exponentially Weighted Moving-Average Control Chart, p.462 -- 15.8.2 Cumulative Sum Control Chart, p.465 -- 15.9 Other SPC Problem-Solving Tools, p.471 -- 15.10 Decision Theory, p.473 -- 15.10.1 Decision Models, p.473 -- 15.10.2 Decision Criteria, p.474 -- 15.11 Implementing SPC, p.476 14 Design of Experiments with Several Factors, p.375 -- 14.1 introduction, p.376 -- 14.2 Factorial Experiments, p.378 -- 14.3 Two-Factor Factorial Experiments, p.382 -- 14.3.1 Statistical Analysis, p.382 -- 14.3.2 Model Adequacy Checking, p.386 -- 14.3.3 One Observation per Cell, p.387 -- 14.4 General Factorial Experiments, p.388 -- 14.52 k Factorial Designs, p.390 -- 14.5.1 22 Design, p.390 -- 14 5.2 2k Design for k > 3 Factors, p.396 -- 14.6 Single Replicate of the 2k Design, p.402 -- 14.7 Addition of Center Points to a 2k Design, p.405 -- 14.8 Blocking and Confounding in the 2k Design, p.408 -- 14.9 One-Half Fraction of the 2k Design, p.413 -- 14.10 Smaller Fractions: The 2k~p Fractional Factorial, p.418 -- 14.11 Response Surface Methods and Designs, p.425 -- 15 Statistical Quality Control, p.434 -- Ouality Improvement and Statistics, p.435 -- 15.1.1 Statistical Quality Control, p.436 -- 15.1.2 Statistical Process Control, p.436 -- 15.2 Introduction to Control Charts, p.436 -- 15.2.1 Basic Principles, p.436 -- 15.2.2 Design of a Control Chart, p.440 -- 15.2.3 Rational Subgroups, p.441 -- 15.2.4 Analysis of Patterns on Control Charts, p.442 -- 15.3 X and/? or S Control Charts, p.444 -- 15.4 Control Charts for Individual Measurements, p.450 -- 15.5 Process Capability, p.452 -- 15.6 Attribute Control Charts, p.456 -- 15.6.1 P Chart (Control Chart for Proportions), p.456 -- 15.6.2 U Chart (Control Chart for Defects per Unit), p.458 -- 15.7 Control Chart Performance, p.460 -- 15.8 Time-Weighted Charts, p.462 -- 15.8.1 Exponentially Weighted Moving-Average Control Chart, p.462 -- 15.8.2 Cumulative Sum Control Chart, p.465 -- 15.9 Other SPC Problem-Solving Tools, p.471 -- 15.10 Decision Theory, p.473 -- 15.10.1 Decision Models, p.473 -- 15.10.2 Decision Criteria, p.474 -- 15.11 Implementing SPC, p.476 -- APPENDIX A Statistical Tables and Charts -- Table I Summary of Common Probability Distributions A-4 -- Table II Cumulative Binomial Probabilities P(X < x) A-5 -- Table II Cumulative Standard Normal Distribution A-8 -- Table IV Percentage Points /2 v of the Chi-Square Distribution A-10 -- Table V Percentage Points ta v of the t Distribution A-ll -- Table VI Percentage Points fa Vj of the F Distribution A-12 -- Table VII Operating Characteristic Curves A-17 -- Table VIII Critical Values for the Sign Test A-26 -- Table IX Critical Values for the Wilcoxon Signed-Rank Test A-26 -- Table X Critical Values for the Wilcoxon Rank-Sum Test A-27 -- Table XI Factors for Constructing Variables Control Charts A-28 -- TableXII Factors for Tolerance Intervals A-29 -- APPENDIX B Bibliography A-31 -- APPENDIX C Summary of Confidence Intervals and Hypothesis Testing Equations for One- and Two Sample Applications A-33 --