Applied statistics and probability for engineers /

Includes bibliographical references and index.

The Role of Statistics in Engineering -- The Engineering Method and Statistical Thinking -- Variability -- Populations and Samples -- Collecting Engineering Data -- Basic Principles -- Retrospective Study -- Observational Study -- Designed Experiments -- Observing Processes over Time -- Mechanistic and Empirical Models -- Probability and Probability Models -- Probability -- Sample Spaces and Events -- Random Experiments -- Sample Spaces -- Events -- Counting Techniques -- Interpretations and Axioms of Probability -- Unions of Events and Addition Rules -- Conditional Probability -- Intersections of Events and Multiplication and Total Probability Rules -- Independence -- Bayes’ Theorem -- Random Variables -- Discrete Random Variables and Probability Distributions -- Probability Distributions and Probability Mass Functions -- Cumulative Distribution Functions -- Mean and Variance of a Discrete Random Variable -- Discrete Uniform Distribution -- Binomial Distribution -- Geometric and Negative Binomial Distributions -- Hypergeometric Distribution -- Poisson Distribution -- Continuous Random Variables and Probability Distributions -- Probability Distributions and Probability Density Functions -- Cumulative Distribution Functions -- Mean and Variance of a Continuous Random Variable -- Continuous Uniform Distribution -- Normal Distribution -- Normal Approximation to the Binomial and Poisson Distributions -- Exponential Distribution -- Erlang and Gamma Distributions -- Weibull Distribution -- Lognormal Distribution -- Beta Distribution -- Joint Probability Distributions -- Joint Probability Distributions for Two Random Variables -- Conditional Probability Distributions and Independence -- Joint Probability Distributions for More Than Two Random Variables -- Covariance and Correlation -- Common Joint Distributions -- Multinomial Probability Distribution -- Bivariate Normal Distribution -- Linear Functions of Random Variables -- General Functions of Random Variables -- Moment-Generating Functions -- Descriptive Statistics -- Numerical Summaries of Data -- Stem-and-Leaf Diagrams -- Frequency Distributions and Histograms -- Box Plots -- Time Sequence Plots -- Scatter Diagrams -- Probability Plots -- Point Estimation of Parameters and Sampling Distributions -- Point Estimation -- Sampling Distributions and the Central Limit Theorem -- General Concepts of Point Estimation -- Unbiased Estimators -- Variance of a Point Estimator -- Standard Error: Reporting a Point Estimate -- Bootstrap Standard Error -- Mean Squared Error of an Estimator -- Methods of Point Estimation -- Method of Moments -- Method of Maximum Likelihood -- Bayesian Estimation of Parameters -- Statistical Intervals for a Single Sample -- Confidence Interval on the Mean of a Normal Distribution, Variance Known -- Development of the Confidence Interval and Its Basic Properties -- Choice of Sample Size -- One-Sided Confidence Bounds -- General Method to Derive a Confidence Interval -- Large-Sample Confidence Interval for μ -- Confidence Interval on the Mean of a Normal Distribution, Variance Unknown -- t Distribution -- t Confidence Interval on μ -- Confidence Interval on the Variance and Standard Deviation of a Normal Distribution -- Large-Sample Confidence Interval for a Population Proportion -- Guidelines for Constructing Confidence Intervals -- Bootstrap Confidence Interval -- Tolerance and Prediction Intervals -- Prediction Interval for a Future Observation -- Tolerance Interval for a Normal Distribution -- Tests of Hypotheses for a Single Sample -- Hypothesis Testing -- Statistical Hypotheses -- Tests of Statistical Hypotheses -- One-Sided and Two-Sided Hypotheses -- P-Values in Hypothesis Tests -- Connection between Hypothesis Tests and Confidence Intervals -- General Procedure for Hypothesis Tests -- Tests on the Mean of a Normal Distribution, Variance Known -- Hypothesis Tests on the Mean -- Type II Error and Choice of Sample Size -- Large-Sample Test -- Tests on the Mean of a Normal Distribution, Variance Unknown -- Hypothesis Tests on the Mean -- Type II Error and Choice of Sample Size -- Tests on the Variance and Standard Deviation of a Normal Distribution -- Hypothesis Tests on the Variance -- Type II Error and Choice of Sample Size -- Tests on a Population Proportion -- Large-Sample Tests on a Proportion -- Type II Error and Choice of Sample Size -- Summary Table of Inference Procedures for a Single Sample -- Testing for Goodness of Fit -- Contingency Table Tests -- Nonparametric Procedures -- The Sign Test -- The Wilcoxon Signed-Rank Test -- Comparison to the t-Test -- Equivalence Testing -- Combining P-Values -- Statistical Inference for Two Samples -- Inference on the Difference in Means of Two Normal Distributions, Variances Known -- Hypothesis Tests on the Difference in Means, Variances Known -- Type II Error and Choice of Sample Size -- Confidence Interval on the Difference in Means, Variances Known -- Inference on the Difference in Means of Two Normal Distributions, Variances Unknown -- Hypotheses Tests on the Difference in Means, Variances Unknown -- Type II Error and Choice of Sample Size -- Confidence Interval on the Difference in Means, Variances Unknown -- A Nonparametric Test for the Difference in Two Means -- Description of the Wilcoxon Rank-Sum Test -- Large-Sample Approximation -- Comparison to the t-Test -- Paired t-Test -- Inference on the Variances of Two Normal Distributions -- F Distribution -- Hypothesis Tests on the Equity of Two Variances -- Type II Error and Choice of Sample Size -- Confidence Interval on the Ratio of Two Variances -- Inference on Two Population Proportions -- Large-Sample Tests on the Difference in Population Proportions -- Type II Error and Choice of Sample Size -- Confidence Interval on the Difference in Population Proportions -- Summary Table and Road Map for Inference Procedures for Two Samples -- Simple Linear Regression and Correlation -- Empirical Models -- Simple Linear Regression -- Properties of the Least Squares Estimators -- Hypothesis Tests in Simple Linear Regression -- Use of t-Tests -- Analysis of Variance Approach to Test Significance of Regression -- Confidence Intervals -- Confidence Intervals on the Slope and Intercept -- Confidence Interval on the Mean Response -- Prediction of New Observations -- Adequacy of the Regression Model -- Residual Analysis -- Coefficient of Determination (R2) -- Correlation -- Regression on Transformed Variables -- Logistic Regression -- Multiple Linear Regression -- Multiple Linear Regression Model -- Introduction -- Least Squares Estimation of the Parameters -- Matrix Approach to Multiple Linear Regression -- Properties of the Least Squares Estimators -- Hypothesis Tests in Multiple Linear Regression -- Test for Significance of Regression -- Tests on Individual Regression Coefficients and Subsets of Coefficients -- Confidence Intervals in Multiple Linear Regression -- Confidence Intervals on Individual Regression Coefficients -- Confidence Interval on the Mean Response -- Prediction of New Observations -- Model Adequacy Checking -- Residual Analysis -- Influential Observations -- Aspects of Multiple Regression Modeling -- Polynomial Regression Models -- Categorical Regressors and Indicator Variables -- Selection of Variables and Model Building -- Multicollinearity -- Design and Analysis of Single-Factor Experiments: The Analysis of Variance -- Designing Engineering Experiments -- Completely Randomized Single-Factor Experiment -- Example: Tensile Strength -- Analysis of Variance -- Multiple Comparisons Following the ANOVA -- Residual Analysis and Model Checking -- Determining Sample Size -- The Random-Effects Model -- Fixed Versus Random Factors -- ANOVA and Variance Components -- Randomized Complete Block Design -- Design and Statistical Analysis -- Multiple Comparisons -- Residual Analysis and Model Checking -- Design of Experiments with Several Factors -- Introduction -- Factorial Experiments -- Two-Factor Factorial Experiments -- Statistical Analysis -- Model Adequacy Checking -- One Observation per Cell -- General Factorial Experiments -- 2k Factorial Designs -- 22 Design -- 2k Design for k ≥ 3 Factors -- Single Replicate of the 2k Design -- Addition of Center Points to a 2k Design -- Blocking and Confounding in the 2k Design -- One-Half Fraction of the 2k Design -- Smaller Fractions: The 2k−p Fractional Factorial -- Response Surface Methods and Designs -- Statistical Quality Control -- Quality Improvement and Statistics -- Statistical Quality Control -- Statistical Process Control -- Introduction to Control Charts -- Basic Principles -- Design of a Control Chart -- Rational Subgroups -- Analysis of Patterns on Control Charts -- X and R or S Control Charts -- Control Charts for Individual Measurements -- Process Capability -- Attribute Control Charts -- P Chart (Control Chart for Proportions) -- U Chart (Control Chart for Defects per Unit) -- Control Chart Performance -- Time-Weighted Charts -- Exponentially Weighted Moving-Average Control Chart -- Cumulative Sum Control Chart -- Other SPC Problem-Solving Tools -- Decision Theory -- Decision Models -- Decision Criteria -- Implementing SPC -- Appendix A Statistical Tables and Charts -- Table I Summary of Common Probability Distributions -- Table II Cumulative Binomial Probabilities P(X ≤ x) -- Table III Cumulative Standard Normal Distribution -- Table IV Percentage Points χ2 α,v of the Chi-Squared Distribution -- Table V Percentage Points tα,v of the t Distribution -- Table VI Percentage Points fα,v1,v2 of the F Distribution -- Chart VII Operating Characteristic Curves -- Table VIII Critical Values for the Sign Test -- Table IX Critical Values for the Wilcoxon Signed-Rank Test -- Table X Critical Values for the Wilcoxon Rank-Sum Test -- Table XI Factors for Constructing Variables Control Charts -- Table XII Factors for Tolerance Intervals -- Appendix B Bibliography -- Appendix C Summary of Confidence Intervals and Hypothesis Testing Equations for One and Two Sample Applications -- Glossary -- Index.