- Emphasizes risk and reliability for the engineering statistics market from a practical point of view
- Includes various applications in engineering
- Provides additional material on simulation, the mathematics related to uncertainty, the rand function, sample variability, dependence, the Poisson process, and more
- Contains additional illustrations on histogram samples and hypothesis testing along with Venn diagrams for conditional probabilities

*Solutions manual and PowerPoint slides available with qualifying course adoption*

In a technological society, virtually every engineer and scientist needs to be able to collect, analyze, interpret, and properly use vast arrays of data. This means acquiring a solid foundation in the methods of data analysis and synthesis. Understanding the theoretical aspects is important, but learning to properly apply the theory to real-world problems is essential.

**Probability, Statistics, and Reliability for Engineers and Scientists, Third Edition** introduces the fundamentals of probability, statistics, reliability, and risk methods to engineers and scientists for the purposes of data and uncertainty analysis and modeling in support of decision making.

The third edition of this bestselling text presents probability, statistics, reliability, and risk methods with an ideal balance of theory and applications. Clearly written and firmly focused on the practical use of these methods, it places increased emphasis on simulation, particularly as a modeling tool, applying it progressively with projects that continue in each chapter. This provides a measure of continuity and shows the broad use of simulation as a computational tool to inform decision making processes. This edition also features expanded discussions of the analysis of variance, including single- and two-factor analyses, and a thorough treatment of Monte Carlo simulation. The authors not only clearly establish the limitations, advantages, and disadvantages of each method, but also show that data analysis is a continuum rather than the isolated application of different methods.

Like its predecessors, this book continues to serve its purpose well as both a textbook and a reference. Ultimately, readers will find the content of great value in problem solving and decision making, particularly in practical applications.

**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 TablesAppendix B: Taylor Series ExpansionAppendix C: Data for Simulation ProjectsAppendix D: Semester Simulation Project**

**Index**

*Problems appear at the end of each chapter.*

**Bilal M. Ayyub** is a professor of civil and environmental engineering and the director of the Center for Technology and Systems Management in the A. James Clark School of Engineering at the University of Maryland, where he has been since 1983. He is a leading authority in risk analysis, uncertainty modeling, decision analysis, and systems engineering. Dr. Ayyub earned degrees from Kuwait University and the Georgia Institute of Technology. He is a fellow of the ASCE, the ASME, and the SNAME, and a senior member of the IEEE. Dr. Ayyub has served on many national committees and investigation boards and completed numerous research and development projects for governmental and private entities, including the National Science Foundation; the U.S. Air Force, Coast Guard, Army Corps of Engineers, Navy, and Department of Homeland Security; and insurance and engineering firms. He has received multiple ASNE Jimmie Hamilton Awards for best papers in the *Naval Engineers Journal*, the ASCE Outstanding Research-Oriented Paper in the *Journal of Water Resources Planning and Management*, the ASCE Edmund Friedman Award, the ASCE Walter Huber Research Prize, the K.S. Fu Award of NAFIPS, and the Department of the Army Public Service Award. Dr. Ayyub is the author/co-author of more than 550 publications in journals, conference proceedings, and reports, as well as 20 books, including *Uncertainty Modeling and Analysis for Engineers and Scientists*; *Risk Analysis in Engineering and Economics*; *Elicitation of Expert Opinions for Uncertainty and Risks*; *Probability, Statistics and Reliability for Engineers and Scientists, Second Edition*; and *Numerical Methods for Engineers*.

**Richard H. McCuen **is the Ben Dyer Professor of civil and environmental engineering at the University of Maryland. Dr. McCuen earned degrees from Carnegie Mellon University and the Georgia Institute of Technology. His primary research interests are statistical hydrology and stormwater management. He has received the Icko Iben Award from the American Water Resource Association and was co-recipient of the Outstanding Research Award from the ASCE Water Resources, Planning and Management Division. He is the author/co-author of over 250 professional papers and 21 books, including *Fundamentals of Civil Engineering: An Introduction to the ASCE Body of Knowledge; Modeling Hydrologic Change*; *Hydrologic Analysis and Design, Third Edition*; *The Elements of Academic Research*; *Estimating Debris Volumes for Flood Control*; and *Dynamic Communication for Engineers*.