Random Phenomena: Fundamentals of Probability and Statistics for Engineers

Prelude Approach Philosophy Four Basic Principles I Foundations Two Motivating Examples Yield Improvement in a Chemical Process Quality Assurance in a Glass Sheet Manufacturing Process Outline of a Systematic Approach Random Phenomena, Variability, and Uncertainty Two Extreme Idealizations of Natural Phenomena Random Mass Phenomena Introducing Probability The Probabilistic Framework II Probability Fundamentals of Probability Theory Building Blocks Operations Probability Conditional Probability Independence Random Variables and Distributions Distributions Mathematical Expectation Characterizing Distributions Special Derived Probability Functions Multidimensional Random Variables Distributions of Several Random Variables Distributional Characteristics of Jointly Distributed Random Variables Random Variable Transformations Single Variable Transformations Bivariate Transformations General Multivariate Transformations Application Case Studies I: Probability Mendel and Heredity World War II Warship Tactical Response Under Attack III Distributions Ideal Models of Discrete Random Variables The Discrete Uniform Random Variable The Bernoulli Random Variable The Hypergeometric Random Variable The Binomial Random Variable Extensions and Special Cases of the Binomial Random Variable The Poisson Random Variable Ideal Models of Continuous Random Variables Gamma Family Random Variables Gaussian Family Random Variables Ratio Family Random Variables Information, Entropy, and Probability Models Uncertainty and Information Entropy Maximum Entropy Principles for Probability Modeling Some Maximum Entropy Models Maximum Entropy Models from General Expectations Application Case Studies II: In-Vitro Fertilization In-Vitro Fertilization and Multiple Births Probability Modeling and Analysis Binomial Model Validation Problem Solution: Model-Based IVF Optimization and Analysis Sensitivity Analysis IV Statistics Introduction to Statistics From Probability to Statistics Variable and Data Types Graphical Methods of Descriptive Statistics Numerical Descriptions Sampling The Distribution of Functions of Random Variables Sampling Distribution of the Mean Sampling Distribution of the Variance Estimation Criteria for Selecting Estimators Point Estimation Methods Precision of Point Estimates Interval Estimates Bayesian Estimation Hypothesis Testing Basic Concepts Concerning Single Mean of a Normal Population Concerning Two Normal Population Means Determining ss, Power, and Sample Size Concerning Variances of Normal Populations Concerning Proportions Concerning Non-Gaussian Populations Likelihood Ratio Tests Discussion Regression Analysis Simple Linear Regression "Intrinsically" Linear Regression Multiple Linear Regression Polynomial Regression Probability Model Validation Probability Plots Chi-Squared Goodness-of-Fit Test Nonparametric Methods Single Population Two Populations Probability Model Validation A Comprehensive Illustrative Example Design of Experiments Analysis of Variance Single Factor Experiments Two-Factor Experiments General Multi-factor Experiments 2k Factorial Experiments and Design Screening Designs: Fractional Factorial Screening Designs: Plackett-Burman 1Response Surface Methodology Introduction to Optimal Designs Application Case Studies III: Statistics Prussian Army Death-by-Horse Kicks WW II Aerial Bombardment of London US Population Dynamics: 1790-2000 Process Optimization V Applications Reliability and Life Testing System Reliability System Lifetime and Failure-Time Distributions The Exponential Reliability Model The Weibull Reliability Model Life Testing Quality Assurance and Control Acceptance Sampling Process and Quality Control Chemical Process Control Process and Parameter Design Introduction to Multivariate Analysis Multivariate Probability Models Multivariate Data Analysis Principal Components Analysis Appendix Index