Introduction to Reliability Analysis: Probability Models and Statistical Methods

by Shelemyahu Zacks

Overview

Reliability analysis is concerned with the analysis of devices and systems whose individual components are prone to failure. This textbook presents an introduction to reliability analysis of repairable and non-repairable systems. It is based on courses given to both undergraduate and graduate students of engineering and statistics as well as in workshops for professional engineers and scientists. As aresult, the book concentrates on the methodology of the subject and on understanding theoretical results rather than on its theoretical development. An intrinsic aspect of reliability analysis is that the failure of components is best modelled using techniques drawn from probability and statistics. Professor Zacks covers all the basic concepts required from these subjects and covers the main modern reliability analysis techniques thoroughly. These include: the graphical analysis of life data, maximum likelihood estimation and bayesian likelihood estimation. Throughout the emphasis is on the practicalities of the subject with numerous examples drawn from industrial and engineering settings.

Product Details

ISBN-13:	9781461276975
Publisher:	Springer New York
Publication date:	10/12/2011
Series:	Springer Texts in Statistics
Edition description:	Softcover reprint of the original 1st ed. 1992
Pages:	212
Product dimensions:	6.10(w) x 9.25(h) x (d)

Table of Contents

1. System Effectiveness.- 1.1 Basic Concepts and Relationships.- 1.2 Time Categories.- 1.3 Reliability and Related Functions.- 1.4 Availability, Maintainability and Repairability.- 1.5 Exercises.- 2. Life Distributions, Models and Their Characteristics.- 2.1 Types of Failure Observations.- 2.2 General Characteristics of Life Distributions.- 2.3 Some Families of Life Distributions.- 2.3.1 Exponential and Shifted Exponential Distributions.- 2.3.2 Erlang, Chi-Square and Gamma Distributions.- 2.3.3 Weibull Distributions.- 2.3.4 Extreme Value Distributions.- 2.3.5 The Normal and Truncated Normal Distributions.- 2.3.6 Normal Approximations.- 2.3.7 Lognormal Distributions.- 2.3.8 Auxiliary Distributions: t and F.- 2.4 Discrete Distributions of Failure Counts.- 2.4.1 Distributions of Discrete Random Variables.- 2.4.2 The Binomial Distribution.- 2.4.3 The Poisson Distribution.- 2.4.4 Hypergeometric Distributions.- 2.5 Exercises.- 3. Reliability of Composite Systems.- 3.1 System Reliability for Series and Active Parallel Independent Components.- 3.2 k Out of n Systems of Independent Components.- 3.3 The Decomposition Method.- 3.4 Minimal Paths and Cuts.- 3.5 The MTTF of Composite Systems.- 3.6 Sequentially Operating Components.- 3.7 Fault Tree Analysis.- 3.8 Exercises.- 4. Reliability of Repairable Systems.- 4.1 The Renewal Process.- 4.2 The Renewal Function and Its Density.- 4.3 Asymptotic Approximations.- 4.4 Increasing the Availability by Preventive Maintenance and Standby Systems.- 4.4.1 Systems with Standby and Repair.- 4.4.2 Preventive Maintenance.- 4.5 Exercises.- 5. Graphical Analysis of Life Data.- 5.1 Probability Plotting for Parametric Models with Uncensored Data.- 5.2 Probability Plotting with Censored Data.- 5.3 Non-Parametric Plotting.- 5.3.1 Product Limit Estimator of Reliability.- 5.3.2 Total Time on Test Plots.- 5.4 Graphical Aids.- 5.5 Exercises.- 6. Estimation of Life Distributions and System Characteristics.- 6.1 Properties of Estimators.- 6.1.1 The Estimation Problem.- 6.1.2 Sampling Distributions, Accuracy and Precision.- 6.1.3 Closeness Probabilities.- 6.1.4 Confidence and Prediction Intervals.- 6.1.4.1 Estimating the Parameters of a Normal Distribution.- 6.1.4.2 Estimating the Reliability Function for an Exponential Distribution.- 6.2 Maximum Likelihood Estimation.- 6.2.1 Single-Parameter Distributions.- 6.2.1.1 Derivation.- 6.2:1.2 The Invariance Property.- 6.2.1.3 The Variance of an MLE.- 6.2.2 Multiparameter Distributions.- 6.3 MLE of System Reliability.- 6.4 MLE from Censored Samples—Exponential Life Distributions.- 6.4.1 Type I Censored Data.- 6.4.2 Type II Censored Data.- 6.5 The Kaplan-Meier PL Estimator as an MLE of R(t): Non-Parametric Approach.- 6.6 Exercises.- 7. Maximum Likelihood Estimators and Confidence Intervals for Specific Life Distributions.- 7.1 Exponential Distributions.- 7.2 Shifted Exponential Distributions.- 7.3 Erlang Distributions.- 7.4 Gamma Distributions.- 7.5 Weibull Distributions.- 7.6 Extreme Value Distributions.- 7.7 Normal and Lognormal Distributions.- 7.8 Truncated Normal Distributions.- 7.9 Exercises.- 8. Bayesian Reliability Estimation and Prediction.- 8.1 Prior and Posterior Distributions.- 8.2 Loss Functions and Bayes Estimators.- 8.2.1 Distribution-Free Bayes Estimator of Reliability.- 8.2.2 Bayes Estimator of Reliability for Exponential Life Distributions.- 8.3 Bayesian Credibility and Prediction Intervals.- 8.3.1 Distribution-Free Reliability Estimation.- 8.3.2 Exponential Reliability Estimation.- 8.3.3 Prediction Intervals.- 8.4 Credibility Intervals for the Asymptotic Availability of Repairable Systems: The Exponential Case.- 8.5 Empirical Bayes Method.- 8.6 Exercises.- 9. Reliability Demonstration: Testing and Acceptance Procedures.- 9.1 Reliability Demonstration.- 9.2 Binomial Testing.- 9.3 Exponential Distributions.- 9.4 Sequential Reliability Testing.- 9.4.1 The SPRT for Binomial Data.- 9.4.2 The SPRT for Exponential Lifetimes.- 9.5 Sequential Tests for Poisson Processes.- 9.6 Bayesian Reliability Demonstration Tests.- 9.7 Accelerated Life Testing.- 9.8 Exercises.- Annotated Bibliography.- Appendix of Statistical Tables.

Editorial Reviews

"This is a nice book which touches on diverse subjects in the area of reliability theory... Particularly impressive is the abundance of numerical examples which illustrate in detail almost all the procedures... a welcome addition..."
(Zentralblatt fuer Mathematik)

From the Publisher

A textbook for graduate and undergraduate students of engineering and statistics. Introduces the methodology of analyzing devices and systems whose components are prone to failure. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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