Probability, Reliability, and Statistical Methods in Engineering Design

by Haldar, Achintya; Mahadevan, Sankaran

• ISBN13: 9780471331193
• ISBN10: 0471331198
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-11-15
• Publisher: Wiley

Summary

Learn the tools to assess product reliability! Haldar and Mahadevan crystallize the research and experience of the last few decades into the most up-to-date book on risk-based design concepts in engineering available. The fundamentals of reliability and statistics necessary for risk-based engineering analysis and design are clearly presented. And with the help of many practical examples integrated throughout the text, the material is made very relevant to today's practice. Key Features * Covers all the fundamental concepts and mathematical skills needed to conduct reliability assessments. * Presents the most widely-used reliability assessment methods. * Concepts that are required for the implementation of risk-based design in practical problems are developed gradually. * Both risk-based and deterministic design concepts are included to show the transition from traditional to modern design practice.

Author Biography

Achintya Haldar, PhD, is a professor in the Department of Civil Engineering and Engineering Mechanics at the University of Arizona, Tucson.

Sankaran Mahadevan, PhD, is Associate Professor of Civil and Environmental Engineering at Vanderbilt University in Nashville, Tennessee.

Table of Contents

Basic Concept of Reliability	1	(9)
Introductory Comments	1	(1)
What Is Reliability?	1	(2)
Need for Reliability Evaluation	3	(1)
Measures of Reliability	4	(1)
Factors Affecting Reliability Evaluation	4	(2)
Sources of Uncertainty	5	(1)
Steps in the Modeling of Uncertainty	6	(1)
Concluding Remarks	7	(2)
Mathematics of Probability	9	(26)
Introductory Comments	9	(1)
Introduction to Set Theory	9	(7)
Elements of Set Theory	9	(3)
Venn Diagram	12	(1)
Combinations of Events	12	(2)
Operational Rules	14	(1)
De Morgan's Rule	15	(1)
Axioms of Probability	16	(4)
Multiplication Rule	20	(5)
Theorem of Total Probability	25	(1)
Bayes' Theorem	25	(3)
Review	28	(1)
Concluding Remarks	29	(1)
Problems	29	(6)
Modeling of Uncertainty	35	(28)
Introductory Comments	35	(1)
Steps in Quantifying Randomness	35	(5)
Data Collection	35	(1)
Descriptors of Randomness	36	(2)
Histogram and Frequency Diagram	38	(2)
Analytical Models to Quantify Randomness	40	(9)
Continuous Random Variables	40	(3)
Discrete Random Variables	43	(2)
General Definitions for Uncertainty Descriptors	45	(3)
Mode and Median	48	(1)
Percentile Value	48	(1)
Multiple Random Variables	49	(9)
Joint Distributions	49	(1)
Conditional PDF and PMF	50	(1)
Marginal PDF and PMF	51	(1)
Covariance and Correlation	51	(7)
Multivariate Distributions	58	(1)
Concluding Remarks	58	(1)
Problems	58	(5)
Commonly Used Probability Distributions	63	(43)
Introductory Comments	63	(1)
Continuous Random Variables	63	(11)
Normal or Gaussian Distribution	64	(4)
Lognormal Random Variables	68	(4)
Beta Distribution	72	(2)
Discrete Random Variables	74	(9)
Binomial Distribution	74	(2)
Geometric Distribution	76	(1)
Return Period	76	(1)
Poisson Distribution	77	(3)
Exponential Distribution	80	(3)
A Combination of Continuous and Discrete Random Variables: Hypergeometric and Hyperbinomial Distributions	83	(4)
Extreme Value Distributions	87	(11)
Introduction	87	(1)
Concept of Extreme Value Distributions	88	(1)
Asymptotic Distributions	89	(1)
The Type I Extreme Value Distribution	89	(2)
The Type II Extreme Value Distribution	91	(3)
The Type III Extreme Value Distribution	94	(3)
Special Cases of Two-Parameter Weibull Distribution	97	(1)
Other Useful Distributions	98	(1)
Concluding Remarks	98	(1)
Problems	99	(7)
Determination of Distributions and Parameters from Observed Data	106	(32)
Introductory Comments	106	(1)
Determination of Probability Distribution	106	(11)
Probability Papers	107	(1)
Construction of a Probability Paper	107	(5)
Statistical Tests	112	(5)
Estimation of Parameters of a Distribution	117	(3)
Method of Moments	117	(1)
Method of Maximum Likelihood	118	(2)
Interval Estimation of Mean and Variance	120	(14)
Interval Estimation for the Mean with Known Variance	121	(4)
Lower and Upper Confidence Limit for the Mean with Known Variance	125	(1)
Interval Estimation for the Mean with Unknown Variance	126	(3)
Lower and Upper Confidence Limit for the Mean with Unknown Variance	129	(1)
Sample Sizes in Estimating the Confidence Interval of Mean	130	(1)
Interval Estimation for the Variance	131	(3)
Concluding Remarks	134	(1)
Problems	134	(4)
Randomness in Response Variables	138	(43)
Introductory Comments	138	(1)
Known Functional Relationship Between the Response and a Single Basic Random Variable	139	(3)
Linear Relationship	139	(1)
Nonlinear Relationship	140	(2)
Response as a Known Function of Multiple Random Variables	142	(7)
Exact Solution	142	(7)
Central Limit Theorem	149	(1)
Partial and Approximate Solutions	149	(5)
Partial Uncertainty Analysis: Response as a Linear Function of Multiple Random Variables	149	(1)
Approximate Solution: Response as a General Function of Multiple Random Variables	150	(4)
Multiple Random Variables with Unknown Relationship	154	(2)
Repression Analysis	156	(17)
Simple Linear Regression Analysis	157	(2)
Coefficient of Determination	159	(2)
Residual Analysis	161	(3)
Multiple Linear Regression	164	(4)
Nonlinear Models	168	(5)
Concluding Remarks	173	(1)
Problems	174	(7)
Fundamentals of Reliability Analysis	181	(44)
Introductory Comments	181	(1)
Deterministic and Probabilistic Approaches	181	(1)
Risk and Safety Factors Concept	182	(1)
Risk-Based Design Concept and the Development of the Risk-Based Design Format	183	(10)
Load and Resistance Normal Variables: Single Load Case	184	(2)
Load and Resistance Normal Variables: Multiple Load Case	186	(4)
Load and Resistance Lognormal Variables: Single Load Case	190	(1)
Load and Resistance Lognormal Variables: Multiple Load Case	191	(2)
Fundamental Concept of Reliability Analysis	193	(2)
First-Order Reliability Methods (FORM)	195	(24)
First-Order Second-Moment Method (FOSM) or MVFOSM Method	195	(3)
AFOSM Method for Normal Variables (Hasofer-Lind Methods)	198	(6)
AFOSM Method for Nonnormal Variables	204	(15)
Risk-Based Design Format Using FORM	219	(3)
Concluding Remarks	222	(1)
Problems	223	(2)
Advanced Topics on Reliability Analysis	225	(25)
Introductory Comments	225	(1)
Second-Order Reliability Methods (SORM)	225	(6)
Reliability Analysis with Correlated Variables	231	(6)
Correlated Normal Variables	233	(1)
Correlated Nonnormal Variables	234	(3)
Probabilistic Sensitivity Indices	237	(1)
System Reliability Evaluation	238	(9)
Series Systems or Weakest Link Systems	240	(3)
Parallel Systems	243	(2)
Nonlinear System Reliability	245	(2)
Implicit Performance Functions	247	(1)
Concluding Remarks	248	(1)
Problems	248	(2)
Simulation Techniques	250	(25)
Introductory Comments	250	(1)
Monte Carlo Simulation Technique	251	(10)
Formulation of the Problem	251	(1)
Quantifying the Probabilistic Characteristics of Random Variables	251	(1)
Generation of Random Numbers	252	(4)
Numerical Experimentation	256	(2)
Extracting Probabilistic Information Using Simulation	258	(1)
Accuracy and Efficiency of Simulation	258	(3)
Variance Reduction Techniques	261	(5)
VRTs in Sampling Methods	262	(3)
Correlation-Based VRTs	265	(1)
Combined Conditional Expectation and Antithetic Variates Method	265	(1)
Simulation of Correlated Random Variables	266	(5)
Simulation of Correlated Normal Variables	268	(2)
Simulation of Correlated Nonnormal Variables	270	(1)
Concluding Remarks	271	(1)
Problems	272	(3)
Appendix 1 Table of the CDF of the Standard Normal Distribution	275	(3)
Appendix 2 Evaluation of Gamma Function	278	(2)
Appendix 3 Table of the CDF of the Chi-Square Distribution with f Degrees of Freedom	280	(2)
Appendix 4 Values of Dαn for the Kolkmogorov-Smirnov (K-S) Test	282	(1)
Appendix 5 Table of the CDF of Student's t-Distribution	283	(2)
Appendix 6 Gram-Schmidt Orthogonalization	285	(2)
Conversion Factors	287	(1)
References	288	(8)
Index	296