Applied Statistics and Probability for Engineers, EMEA Edition

Häftad, Engelska, 2019

Av Douglas C. Montgomery, George C. Runger, Douglas C. (Georgia Institute of Technology) Montgomery, George C. (Rensselaer Polytechnic Institute) Runger

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Applied Statistics and Probability for Engineers provides a practical approach to probability and statistical methods. Students learn how the material will be relevant in their careers by including a rich collection of examples and problem sets that reflect realistic applications and situations. This product focuses on real engineering applications and real engineering solutions while including material on the bootstrap, increased emphasis on the use of p-value, coverage of equivalence testing, and combining p-values. The content, examples, exercises and answers presented in this product have been meticulously checked for accuracy.

Produktinformation

Utgivningsdatum2019-07-26
Mått10 x 10 x 10 mm
Vikt454 g
FormatHäftad
SpråkEngelska
Antal sidor720
Upplaga7
FörlagJohn Wiley & Sons Inc
ISBN9781119585596

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1 The Role of Statistics in Engineering 11.1 The Engineering Method and Statistical Thinking 21.1.1 Variability 31.1.2 Populations and Samples 51.2 Collecting Engineering Data 51.2.1 Basic Principles 51.2.2 Retrospective Study 51.2.3 Observational Study 61.2.4 Designed Experiments 61.2.5 Observing Processes over Time 91.3 Mechanistic and Empirical Models 121.4 Probability and Probability Models 152 Probability 172.1 Sample Spaces and Events 182.1.1 Random Experiments 182.1.2 Sample Spaces 192.1.3 Events 212.2 Counting Techniques 232.3 Interpretations and Axioms of Probability 262.4 Unions of Events and Addition Rules 292.5 Conditional Probability 312.6 Intersections of Events and Multiplication and Total Probability Rules 342.7 Independence 362.8 Bayes’ Theorem 392.9 Random Variables 403 Discrete Random Variables and Probability Distributions 423.1 Probability Distributions and Probability Mass Functions 433.2 Cumulative Distribution Functions 453.3 Mean and Variance of a Discrete Random Variable 473.4 Discrete Uniform Distribution 493.5 Binomial Distribution 513.6 Geometric and Negative Binomial Distributions 553.7 Hypergeometric Distribution 593.8 Poisson Distribution 634 Continuous Random Variables and Probability Distributions 664.1 Probability Distributions and Probability Density Functions 674.2 Cumulative Distribution Functions 704.3 Mean and Variance of a Continuous Random Variable 714.4 Continuous Uniform Distribution 724.5 Normal Distribution 734.6 Normal Approximation to the Binomial and Poisson Distributions 794.7 Exponential Distribution 834.8 Erlang and Gamma Distributions 864.9 Weibull Distribution 894.10 Lognormal Distribution 904.11 Beta Distribution 925 Joint Probability Distributions 955.1 Joint Probability Distributions for Two Random Variables 965.2 Conditional Probability Distributions and Independence 1025.3 Joint Probability Distributions for More Than Two Random Variables 1075.4 Covariance and Correlation 1105.5 Common Joint Distributions 1135.5.1 Multinomial Probability Distribution 1135.5.2 Bivariate Normal Distribution 1155.6 Linear Functions of Random Variables 1175.7 General Functions of Random Variables 1205.8 Moment-Generating Functions 1216 Descriptive Statistics 1266.1 Numerical Summaries of Data 1276.2 Stem-and-Leaf Diagrams 1316.3 Frequency Distributions and Histograms 1356.4 Box Plots 1396.5 Time Sequence Plots 1406.6 Scatter Diagrams 1426.7 Probability Plots 1447 Point Estimation of Parameters and Sampling Distributions 1487.1 Point Estimation 1497.2 Sampling Distributions and the Central Limit Theorem 1507.3 General Concepts of Point Estimation 1567.3.1 Unbiased Estimators 1567.3.2 Variance of a Point Estimator 1577.3.3 Standard Error: Reporting a Point Estimate 1587.3.4 Bootstrap Standard Error 1597.3.5 Mean Squared Error of an Estimator 1607.4 Methods of Point Estimation 1617.4.1 Method of Moments 1627.4.2 Method of Maximum Likelihood 1637.4.3 Bayesian Estimation of Parameters 1678 Statistical Intervals for a Single Sample 1708.1 Confidence Interval on the Mean of a Normal Distribution, Variance Known 1728.1.1 Development of the Confidence Interval and Its Basic Properties 1728.1.2 Choice of Sample Size 1758.1.3 One-Sided Confidence Bounds 1768.1.4 General Method to Derive a Confidence Interval 1768.1.5 Large-Sample Confidence Interval for μ 1778.2 Confidence Interval on the Mean of a Normal Distribution, Variance Unknown 1798.2.1 t Distribution 1808.2.2 t Confidence Interval on μ 1818.3 Confidence Interval on the Variance and Standard Deviation of a Normal Distribution 1828.4 Large-Sample Confidence Interval for a Population Proportion 1858.5 Guidelines for Constructing Confidence Intervals 1888.6 Bootstrap Confidence Interval 1898.7 Tolerance and Prediction Intervals 1898.7.1 Prediction Interval for a Future Observation 1898.7.2 Tolerance Interval for a Normal Distribution 1919 Tests of Hypotheses for a Single Sample 1939.1 Hypothesis Testing 1949.1.1 Statistical Hypotheses 1949.1.2 Tests of Statistical Hypotheses 1969.1.3 One-Sided and Two-Sided Hypotheses 2029.1.4 P-Values in Hypothesis Tests 2039.1.5 Connection between Hypothesis Tests and Confidence Intervals 2069.1.6 General Procedure for Hypothesis Tests 2069.2 Tests on the Mean of a Normal Distribution, Variance Known 2089.2.1 Hypothesis Tests on the Mean 2089.2.2 Type II Error and Choice of Sample Size 2119.2.3 Large-Sample Test 2159.3 Tests on the Mean of a Normal Distribution, Variance Unknown 2159.3.1 Hypothesis Tests on the Mean 2159.3.2 Type II Error and Choice of Sample Size 2209.4 Tests on the Variance and Standard Deviation of a Normal Distribution 2229.4.1 Hypothesis Tests on the Variance 2229.4.2 Type II Error and Choice of Sample Size 2249.5 Tests on a Population Proportion 2259.5.1 Large-Sample Tests on a Proportion 2259.5.2 Type II Error and Choice of Sample Size 2279.6 Summary Table of Inference Procedures for a Single Sample 2299.7 Testing for Goodness of Fit 2299.8 Contingency Table Tests 2329.9 Nonparametric Procedures 2349.9.1 The Sign Test 2359.9.2 The Wilcoxon Signed-Rank Test 2399.9.3 Comparison to the t-Test 2409.10 Equivalence Testing 2409.11 Combining P-Values 24210 Statistical Inference for Two Samples 24410.1 Inference on the Difference in Means of Two Normal Distributions, Variances Known 24510.1.1 Hypothesis Tests on the Difference in Means, Variances Known 24710.1.2 Type II Error and Choice of Sample Size 24910.1.3 Confidence Interval on the Difference in Means, Variances Known 25110.2 Inference on the Difference in Means of Two Normal Distributions, Variances Unknown 25310.2.1 Hypotheses Tests on the Difference in Means, Variances Unknown 25310.2.2 Type II Error and Choice of Sample Size 25910.2.3 Confidence Interval on the Difference in Means, Variances Unknown 26010.3 A Nonparametric Test for the Difference in Two Means 26110.3.1 Description of the Wilcoxon Rank-Sum Test 26210.3.2 Large-Sample Approximation 26310.3.3 Comparison to the t-Test 26410.4 Paired t-Test 26410.5 Inference on the Variances of Two Normal Distributions 26810.5.1 F Distribution 26810.5.2 Hypothesis Tests on the Equity of Two Variances 27010.5.3 Type II Error and Choice of Sample Size 27210.5.4 Confidence Interval on the Ratio of Two Variances 27310.6 Inference on Two Population Proportions 27310.6.1 Large-Sample Tests on the Difference in Population Proportions 27410.6.2 Type II Error and Choice of Sample Size 27610.6.3 Confidence Interval on the Difference in Population Proportions 27710.7 Summary Table and Road Map for Inference Procedures for Two Samples 27811 Simple Linear Regression and Correlation 28011.1 Empirical Models 28111.2 Simple Linear Regression 28411.3 Properties of the Least Squares Estimators 28811.4 Hypothesis Tests in Simple Linear Regression 28811.4.1 Use of t-Tests 28911.4.2 Analysis of Variance Approach to Test Significance of Regression 29111.5 Confidence Intervals 29211.5.1 Confidence Intervals on the Slope and Intercept 29211.5.2 Confidence Interval on the Mean Response 29311.6 Prediction of New Observations 29511.7 Adequacy of the Regression Model 29611.7.1 Residual Analysis 29611.7.2 Coefficient of Determination (R2) 29811.8 Correlation 29911.9 Regression on Transformed Variables 30311.10 Logistic Regression 30512 Multiple Linear Regression 31012.1 Multiple Linear Regression Model 31112.1.1 Introduction 31112.1.2 Least Squares Estimation of the Parameters 31412.1.3 Matrix Approach to Multiple Linear Regression 31612.1.4 Properties of the Least Squares Estimators 32112.2 Hypothesis Tests in Multiple Linear Regression 32212.2.1 Test for Significance of Regression 32212.2.2 Tests on Individual Regression Coefficients and Subsets of Coefficients 32512.3 Confidence Intervals in Multiple Linear Regression 32912.3.1 Confidence Intervals on Individual Regression Coefficients 32912.3.2 Confidence Interval on the Mean Response 33012.4 Prediction of New Observations 33112.5 Model Adequacy Checking 33312.5.1 Residual Analysis 33312.5.2 Influential Observations 33512.6 Aspects of Multiple Regression Modeling 33712.6.1 Polynomial Regression Models 33712.6.2 Categorical Regressors and Indicator Variables 33912.6.3 Selection of Variables and Model Building 34112.6.4 Multicollinearity 34913 Design and Analysis of Single-Factor Experiments: The Analysis of Variance 35113.1 Designing Engineering Experiments 35213.2 Completely Randomized Single-Factor Experiment 35313.2.1 Example: Tensile Strength 35313.2.2 Analysis of Variance 35413.2.3 Multiple Comparisons Following the ANOVA 35913.2.4 Residual Analysis and Model Checking 36113.2.5 Determining Sample Size 36313.3 The Random-Effects Model 36513.3.1 Fixed Versus Random Factors 36513.3.2 ANOVA and Variance Components 36513.4 Randomized Complete Block Design 36813.4.1 Design and Statistical Analysis 36813.4.2 Multiple Comparisons 37213.4.3 Residual Analysis and Model Checking 37314 Design of Experiments with Several Factors 37514.1 Introduction 37614.2 Factorial Experiments 37814.3 Two-Factor Factorial Experiments 38214.3.1 Statistical Analysis 38214.3.2 Model Adequacy Checking 38614.3.3 One Observation per Cell 38714.4 General Factorial Experiments 38814.5 2k Factorial Designs 39014.5.1 22 Design 39014.5.2 2k Design for k ≥ 3 Factors 39614.6 Single Replicate of the 2k Design 40214.7 Addition of Center Points to a 2k Design 40514.8 Blocking and Confounding in the 2k Design 40814.9 One-Half Fraction of the 2k Design 41314.10 Smaller Fractions: The 2k−p Fractional Factorial 41814.11 Response Surface Methods and Designs 42515 Statistical Quality Control 43415.1 Quality Improvement and Statistics 43515.1.1 Statistical Quality Control 43615.1.2 Statistical Process Control 43615.2 Introduction to Control Charts 43615.2.1 Basic Principles 43615.2.2 Design of a Control Chart 44015.2.3 Rational Subgroups 44115.2.4 Analysis of Patterns on Control Charts 44215.3 X and R or S Control Charts 44415.4 Control Charts for Individual Measurements 45015.5 Process Capability 45215.6 Attribute Control Charts 45615.6.1 P Chart (Control Chart for Proportions) 45615.6.2 U Chart (Control Chart for Defects per Unit) 45815.7 Control Chart Performance 46015.8 Time-Weighted Charts 46215.8.1 Exponentially Weighted Moving-Average Control Chart 46215.8.2 Cumulative Sum Control Chart 46515.9 Other SPC Problem-Solving Tools 47115.10 Decision Theory 47315.10.1 Decision Models 47315.10.2 Decision Criteria 47415.11 Implementing SPC 476APPENDIX A Statistical Tables and Charts A-3Table I Summary of Common Probability Distributions A-4Table II Cumulative Binomial Probabilities P(X ≤ x) A-5Table III Cumulative Standard Normal Distribution A-8Table IV Percentage Points χ2 α,v of the Chi-Squared Distribution A-10Table V Percentage Points tα,v of the t Distribution A-11Table VI Percentage Points fα,v1,v2 of the F Distribution A-12Chart VII Operating Characteristic Curves A-17Table VIII Critical Values for the Sign Test A-26Table IX Critical Values for the Wilcoxon Signed-Rank Test A-26Table X Critical Values for the Wilcoxon Rank-Sum Test A-27Table XI Factors for Constructing Variables Control Charts A-28Table XII Factors for Tolerance Intervals A-29APPENDIX B Bibliography A-31APPENDIX C Summary of Confidence Intervals and Hypothesis Testing Equations for One and Two Sample Applications A-33GLOSSARY G-1INDEX I-1