Probability, Statistics, and Reliability for Engineers and Scientists

by Bilal M. Ayyub, Richard H. McCuen

Overview

Virtually every engineer and scientist must 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.

The goal of this popular and proven book is to introduce the fundamentals of probability, statistics, reliability, and risk methods to engineers and scientists for the purpose of data and uncertainty analysis and modeling in support of decision-making.

The primary objectives to the author's approach include: (1) introducing probability, statistics, reliability, and risk methods to students and practicing professionals in engineering and the sciences; (2) emphasizing the practical use of these methods; and (3) establishing the limitations, advantages, and disadvantages of the methods. The book was developed with an emphasis on solving real-world technological problems that engineers and scientists are asked to solve as part of their professional responsibilities.

Upon graduation, engineers and scientists must have a solid academic foundation in methods of data analysis and synthesis, as the analysis and synthesis of complex systems are common tasks that confront even entry-level professionals.

The underlying theory, especially the assumptions central to the methods, is presented, but then the proper application of the theory is presented through realistic examples, often using actual data. Every attempt is made to show that methods of data analysis are not independent of each other. Instead, we show that real-world problem-solving often involves applying many of the methods presented in different chapters.

Probability, Statistics, and Reliability for Engineers and Scientists, here in its fourth edition, is a very popular textbook. Ultimately, readers will find its content of great value in problem-solving and decision-making, particularly in practical applications.

Product Details

ISBN-13:	9781032967714
Publisher:	CRC Press
Publication date:	05/12/2025
Edition description:	4th ed.
Pages:	638
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

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.

Table of Contents

Chapter 1	Introduction	1
1.1.	Introduction	1
1.2.	Types of Uncertainty	5
1.3.	Introduction to Simulation	9
1.4.	Problems	17
1.5.	Simulation Projects	19
Chapter 2	Data Description and Treatment	25
2.1.	Introduction	26
2.2.	Classification of Data	26
2.3.	Graphical Description of Data	28
2.4.	Histograms and Frequency Diagrams	36
2.5.	Descriptive Measures	39
2.6.	Applications	46
2.7.	Analysis of Simulated Data	49
2.8.	Problems	54
2.9.	Simulation Projects	60
Chapter 3	Fundamentals of Probability	63
3.1.	Introduction	64
3.2.	Sample Spaces, Sets, and Events	64
3.3.	Mathematics of Probability	69
3.4.	Random Variables and their Probability Distributions	83
3.5.	Moments	91
3.6.	Application: Water Supply and Quality	101
3.7.	Simulation and Probability Distributions	102
3.8.	Problems	104
3.9.	Simulation Projects	109
Chapter 4	Probability Distributions for Discrete Random Variables	111
4.1.	Introduction	111
4.2.	Bernoulli Distribution	112
4.3.	Binomial Distribution	113
4.4.	Geometric Distribution	115
4.5.	Poisson Distribution	116
4.6.	Negative Binomial and Pascal Probability Distributions	118
4.7.	Hypergeometric Probability Distribution	118
4.8.	Applications	119
4.9.	Simulation of Discrete Random Variables	121
4.10.	Problems	127
4.11.	Simulation Projects	129
Chapter 5	Probability Distributions for Continuous Random Variables	131
5.1.	Introduction	132
5.2.	Uniform Distribution	132
5.3.	Normal Distribution	134
5.4.	Lognormal Distribution	138
5.5.	Exponential Distribution	141
5.6.	Triangular Distribution	143
5.7.	Gamma Distribution	144
5.8.	Rayleigh Distribution	145
5.9.	Statistical Probability Distributions	146
5.10.	Extreme Value Distributions	149
5.11.	Applications	155
5.12.	Simulation and Probability Distributions	157
5.13.	Problems	160
5.14.	Simulation Projects	161
Chapter 6	Multiple Random Variables	165
6.1.	Introduction	165
6.2.	Joint Random Variables and their Probability Distributions	166
6.3.	Functions of Random Variables	182
6.4.	Applications	192
6.5.	Multivariable Simulation	199
6.6.	Problems	209
6.7.	Simulation Projects	213
Chapter 7	Simulation	215
7.1.	Introduction	216
7.2.	Monte Carlo Simulation	221
7.3.	Random Numbers	222
7.4.	Generation of Random Variables	225
7.5.	Generation of Selected Discrete Random Variables	232
7.6.	Generation of Selected Continuous Random Variables	238
7.7.	Applications	242
7.8.	Problems	252
7.9.	Simulation Projects	257
Chapter 8	Fundamentals of Statistical Analysis	259
8.1.	Introduction	259
8.2.	Estimation of Parameters	261
8.3.	Sampling Distributions	276
8.4.	Applications	280
8.5.	Problems	285
8.6.	Simulation Project	287
Chapter 9	Hypothesis Testing	289
9.1.	Introduction	290
9.2.	General Procedure	290
9.3.	Hypothesis Tests of Means	295
9.4.	Hypothesis Tests of Variances	302
9.5.	Tests of Distributions	308
9.6.	Applications	319
9.7.	Simulation of Hypothesis Test Assumptions	326
9.8.	Problems	328
9.9.	Simulation Projects	333
Chapter 10	Analysis of Variance	335
10.1.	Introduction	335
10.2.	Test of Population Means	336
10.3.	Multiple Comparisons in the ANOVA Test	345
10.4.	Test of Population Variances	349
10.5.	Randomized Block Design	351
10.6.	Two-Way Analysis of Variance	357
10.7.	Applications	370
10.8.	Problems	372
10.9.	Simulation Projects	377
Chapter 11	Confidence Intervals and Sample Size Determination	379
11.1.	Introduction	379
11.2.	General Procedure	380
11.3.	Confidence Intervals on Sample Statistics	381
11.4.	Sample-Size Determination	384
11.5.	Applications	387
11.6.	Problems	389
11.7.	Simulation Projects	391
Chapter 12	Regression Analysis	393
12.1.	Introduction	394
12.2.	Correlation Analysis	394
12.3.	Introduction to Regression	404
12.4.	Principle of Least Squares	409
12.5.	Reliability of the Regression Equation	412
12.6.	Reliability of Point Estimates of the Regression Coefficients	420
12.7.	Confidence Intervals of the Regression Equation	423
12.8.	Correlation vs. Regression	428
12.9.	Applications of Bivariate Regression Analysis	429
12.10.	Simulation and Prediction Models	437
12.11.	Problems	439
12.12.	Simulation Projects	445
Chapter 13	Multiple and Nonlinear Regression Analysis	447
13.1.	Introduction	448
13.2.	Correlation Analysis	448
13.3.	Multiple Regression Analysis	450
13.4.	Polynomial Regression Analysis	459
13.5.	Regression Analysis of Power Models	464
13.6.	Applications	466
13.7.	Simulation in Curvilinear Modeling	478
13.8.	Problems	481
13.9.	Simulation Projects	484
Chapter 14	Reliability Analysis of Components	485
14.1.	Introduction	485
14.2.	Time to Failure	486
14.3.	Reliability of Components	489
14.4.	First-Order Reliability Method	491
14.5.	Advanced Second-Moment Method	496
14.6.	Simulation Methods	509
14.7.	Reliability-Based Design	519
14.8.	Application: Structural Reliability of a Pressure Vessel	525
14.9.	Problems	530
14.10.	Simulation Projects	534
Chapter 15	Reliability and Risk Analysis of Systems	535
15.1.	Introduction	535
15.2.	Reliability of Systems	537
15.3.	Risk Analysis	551
15.4.	Risk-Based Decision Analysis	557
15.5.	Application: System Reliability of a Post-Tensioned Truss	562
15.6.	Problems	565
15.7.	Simulation Projects	568
Chapter 16	Bayesian Methods	569
16.1.	Introduction	569
16.2.	Bayesian Probabilities	570
16.3.	Bayesian Estimation of Parameters	575
16.4.	Bayesian Statistics	584
16.5.	Applications	588
16.6.	Problems	591
Appendix A	Probability and Statistics Tables	595
A-1.	Cumulative Distribution Function of Standard Normal ([Phi](z))	596
A-2.	Critical Values for the student's t Distribution (t[subscript alpha,k])	599
A-3.	Critical Values for the Chi-Square Distribution (c[subscript alpha,k] = X[superscript 2 subscript alpha,k])	601
A-4.	Critical Values for the F Distribution (f[subscript alpha,k,u] = f[subscript alpha, v subscript 1, v subscript 2])	603
A-5.	Critical Values for the Pearson Correlation Coefficient for the Null Hypothesis H[subscript 0]: [rho] = 0 and Both the One-Tailed Alternative H[subscript A]: ##[rho]## > 0 and the Two-Tailed Alternative H[subscript A] : [rho] [not equal] 0	608
A-6.	Uniformly Distributed Random Numbers	609
A-7.	Critical Values for the Kolmogorov-Smirnov One-Sample Test	610
A-8.	Values of the Gamma Function	611
A-9.	Critical Values for the Duncan Multiple Range Test for a 5% Level of Significance and Selected Degrees of Freedom (df) and p Groups	612
Appendix B	Taylor Series Expansion	613
B-1.	Taylor Series	613
B-2.	Common Taylor Series	616
B-3.	Applications: Taylor Series Expansion of the Square Root	617
B-4.	Problems	618
Appendix C	Data for Simulation Projects	621
C-1.	Stream Erosion Study	621
C-2.	Traffic Estimation Study	622
C-3.	Water Evaporation Study	623
	Index	625

Editorial Reviews

Focused on practical aspects, this text introduces probability, statistics, reliability, and risk methods with a balance of theory and applications. Emphasis is placed on simulation, particularly as a modeling tool, applying it to ongoing project examples. This second edition features expanded discussions of the analysis of variance including single- and two-factor analyses and detailed treatment of Monte Carlo simulation. The limitations and advantages of each method are outlined, presenting data analysis as a continuum rather than the isolated application of different methods. Ayyub and McCuen are professors of civil and environmental engineering at the University of Maryland-College Park. Annotation c. Book News, Inc., Portland, OR (booknews.com)