Probability, Statistics, and Reliability for Engineers and Scientists

Introduction Introduction Knowledge, Information, and Opinions Ignorance and Uncertainty Aleatory and Epistemic Uncertainties in System Abstraction Characterizing and Modeling Uncertainty Simulation for Uncertainty Analysis and Propagation Simulation Projects Data Description and Treatment Introduction Classification of Data Graphical Description of Data Histograms and Frequency Diagrams Descriptive Measures Applications Analysis of Simulated Data Simulation Projects Fundamentals of Probability Introduction Sets, Sample Spaces, and Events Mathematics of Probability Random Variables and Their Probability Distributions Moments Application: Water Supply and Quality Simulation and Probability Distributions Simulation Projects Probability Distributions for Discrete Random Variables Introduction Bernoulli Distribution Binomial Distribution Geometric Distribution Poisson Distribution Negative Binomial and Pascal Probability Distributions Hypergeometric Probability Distribution Applications Simulation of Discrete Random Variables A Summary of Distributions Simulation Projects Probability Distributions for Continuous Random Variables Introduction Uniform Distribution Normal Distribution Lognormal Distribution Exponential Distribution Triangular Distribution Gamma Distribution Rayleigh Distribution Beta Distribution Statistical Probability Distributions Extreme Value Distributions Applications Simulation and Probability Distributions A Summary of Distributions Simulation Projects Multiple Random Variables Introduction Joint Random Variables and Their Probability Distributions Functions of Random Variables Modeling Aleatory and Epistemic Uncertainty Applications Multivariable Simulation Simulation Projects Simulation Introduction Monte Carlo Simulation Random Numbers Generation of Random Variables Generation of Selected Discrete Random Variables Generation of Selected Continuous Random Variables Applications Simulation Projects Fundamentals of Statistical Analysis Introduction Properties of Estimators Method-of-Moments Estimation Maximum Likelihood Estimation Sampling Distributions Univariate Frequency Analysis Applications Simulation Projects Hypothesis Testing Introduction General Procedure Hypothesis Tests of Means Hypothesis Tests of Variances Tests of Distributions Applications Simulation of Hypothesis Test Assumptions Simulation Projects Analysis of Variance Introduction Test of Population Means Multiple Comparisons in the ANOVA Test Test of Population Variances Randomized Block Design Two-Way ANOVA Experimental Design Applications Simulation Projects Confidence Intervals and Sample-Size Determination Introduction General Procedure Confidence Intervals on Sample Statistics Sample Size Determination Relationship between Decision Parameters and Types I and II Errors Quality Control Applications Simulation Projects Regression Analysis Introduction Correlation Analysis Introduction to Regression Principle of Least Squares Reliability of the Regression Equation Reliability of Point Estimates of the Regression Coefficients Confidence Intervals of the Regression Equation Correlation versus Regression Applications of Bivariate Regression Analysis Simulation and Prediction Models Simulation Projects Multiple and Nonlinear Regression Analysis Introduction Correlation Analysis Multiple Regression Analysis Polynomial Regression Analysis Regression Analysis of Power Models Applications Simulation in Curvilinear Modeling Simulation Projects Reliability Analysis of Components Introduction Time to Failure Reliability of Components First-Order Reliability Method Advanced Second-Moment Method Simulation Methods Reliability-Based Design Application: Structural reliability of a Pressure Vessel Simulation Projects Reliability and Risk Analysis of Systems Introduction Reliability of Systems Risk Analysis Risk-Based Decision Analysis Application: System Reliability of a Post-Tensioned Truss Simulation Projects Bayesian Methods Introduction Bayesian Probabilities Bayesian Estimation of Parameters Bayesian Statistics Applications Appendix A: Probability and Statistics Tables Appendix B: Taylor Series Expansion Appendix C: Data for Simulation Projects Appendix D: Semester Simulation Project Index Problems appear at the end of each chapter.