This book helps engineering students and practicing engineers understand the fundamentals of probability, statistics, and reliability methods, especially their applications, limitations, and potential.

IntroductionIntroduction
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.