Probability, Statistics, & Reliability for Engineers

by Ayyub, Bilal M.; McCuen, Richard H.

• ISBN13: 9780849326905
• ISBN10: 0849326907
• Additional ISBN(s): 9781584882862
• Format: Hardcover
• Copyright: 1997-06-01
• Publisher: CRC Pr I Llc
• More Book Details
• Purchase Benefits

Summary

Engineers commonly encounter problems that require them to make decisions under conditions of uncertainty. The uncertainty can be in the definition of the problem, the available information, the alternative solutions and their results, or the random nature of the solution outcomes. As engineers are required to solve increasingly complex design problems with limited resources, they must rely more and more on the proper treatment of uncertainty to make the best decisions. Probability, Statistics, and Reliability for Engineers will assist both engineering students and practicing engineers in understanding the fundamentals of probability, statistics, and reliability methods, especially their applications, limitations, and potentials.Full of examples, this practical guide allows engineers to model very complex situations and predict an array of possible outcomes. It will also show readers how to write computational algorithms to solve probability and statistical problems.Among the many examples cited are:· Time to Failure of Cranes· Discharge and Flow of Rivers· Hydraulic Pump Reliability· Predicting Defects in Manufacturing· Nuclear Reactor Reliability· Traffic Flow PatternsFor each chapter in the book, computational examples are given in individual sections, and more detailed engineering applications are presented in a concluding section. Each chapter also includes exercise problems covering the material presented, which will assist readers in practicing the fundamental concepts. Probability, Statistics, and Reliability for Engineers provides a well-rounded introduction to these methods for students in engineering, mathematics, and statistics; practicing engineers in all disciplines; and mathematicians and scientists.

Table of Contents

Chapter 1 Introduction	1	(22)
1.1 Introduction	1	(3)
1.2 Types of Uncertainty	4	(3)
1.3 Taylor Series Expansion	7	(2)
1.4 Applications	9	(3)
1.5 Introduction to Simulation	12	(6)
1.6 Problems	18	(5)
Chapter 2 Data Description and Treatment	23	(32)
2.1 Introduction	23	(1)
2.2 Classification of Data	24	(2)
2.3 Graphical Description of Data	26	(9)
2.4 Histograms and Frequency Diagrams	35	(2)
2.5 Descriptive Measures	37	(6)
2.6 Applications	43	(3)
2.7 Analysis of Simulated Data	46	(4)
2.8 Problems	50	(5)
Chapter 3 Fundamentals of Probability	55	(82)
3.1 Introduction	56	(1)
3.2 Sample Spaces, Sets, and Events	56	(5)
3.3 Mathematics of Probability	61	(11)
3.4 Random Variables and their Probability Distributions	72	(9)
3.5 Moments	81	(9)
3.6 Common Discrete Probability Distributions	90	(7)
3.7 Common Continuous Probability Distributions	97	(19)
3.8 Applications	116	(6)
3.9 Simulation and Probability Distributions	122	(8)
3.10 Problems	130	(7)
Chapter 4 Multiple Random Variables	137	(50)
4.1 Introduction	137	(1)
4.2 Joint Random Variables and their Probability Distributions	138	(18)
4.3 Functions of Random Variables	156	(9)
4.4 Applications	165	(7)
4.5 Multivariable Simulation	172	(10)
4.6 Problems	182	(5)
Chapter 5 Fundamentals of Statistical Analysis	187	(84)
5.1 Introduction	188	(2)
5.2 Estimation of Parameters	190	(15)
5.3 Sampling Distributions	205	(4)
5.4 Hypothesis Testing: Procedure	209	(6)
5.5 Hypothesis Tests of Means	215	(7)
5.6 Hypothesis Tests of Variances	222	(5)
5.7 Confidence Intervals	227	(5)
5.8 Sample-Size Determination	232	(3)
5.9 Selection of Model Probability Distributions	235	(20)
5.10 Applications	255	(8)
5.11 Simulation and Sampling	263	(2)
5.12 Problems	265	(6)
Chapter 6 Regression Analysis	271	(84)
6.1 Introduction	272	(1)
6.2 Correlation Analysis	273	(10)
6.3 Introduction to Regression	283	(4)
6.4 Principle of Least Squares	287	(3)
6.5 Reliability of the Regression Equation	290	(8)
6.6 Reliability of Point Estimates of the Regression Coefficients	298	(3)
6.7 Confidence Intervals of the Regression Equation	301	(5)
6.8 Correlation vs. Regression	306	(2)
6.9 Applications of Bivariate Regression Analysis	308	(7)
6.10 Multiple Regression Analysis	315	(12)
6.11 Regression Analysis of Nonlinear Models	327	(6)
6.12 Applications	333	(13)
6.13 Simulation and Prediction Models	346	(3)
6.14 Problems	349	(6)
Chapter 7 Simulation	355	(38)
7.1 Introduction	355	(6)
7.2 Monte Carlo Simulation	361	(1)
7.3 Random Numbers	362	(3)
7.4 Generation of Random Variables	365	(7)
7.5 Generation of Selected Discrete Random Variables	372	(6)
7.6 Generation of Selected Continuous Random Variables	378	(2)
7.7 Applications	380	(10)
7.8 Problems	390	(3)
Chapter 8 Reliability and Risk Analysis	393	(66)
8.1 Introduction	393	(1)
8.2 Time to Failure	394	(3)
8.3 Reliability of Components	397	(27)
8.4 Reliability of Systems	424	(14)
8.5 Risk-Based Decision Analysis	438	(5)
8.6 Applications	443	(10)
8.7 Problems	453	(6)
Chapter 9 Bayesian Methods	459	(26)
9.1 Introduction	459	(1)
9.2 Bayesian Probabilities	459	(7)
9.3 Bayesian Estimation of Parameters	466	(8)
9.4 Bayesian Statistics	474	(4)
9.5 Applications	478	(4)
9.6 Problems	482	(3)
Appendix A Probability and Statistics Tables	485	(16)
A-1. Cumulative Distribution Function of Standard Normal	486	(3)
A-2. Critical Values for the Student-t Distribution	489	(2)
A-3. Critical Values for the Chi-Square Distribution	491	(2)
A-4. Critical Values for the F Distribution	493	(5)
A-5. Critical Values for the Pearson Correlation Coefficient	498	(1)
A-6. Random Numbers	499	(1)
A-7. Critical Values for the Kolmogorov-Smirnov One-Sample Test	500	(1)
Appendix B Values of the Gamma Function	501	(2)
Index	503