Epstein B., Weissman I. Mathematical Models for Systems Reliability

Chapman & Hall/CRC, Taylor & Francis Group, 2008
ISBN13: 978-1-4200-8082-7This book has evolved from the lectures of Professor Benjamin (Ben) Epstein (1918–2004) at the Technion—Israel Institute of Technology. Throughout his tenure at the Technion, from 1968 until his retirement in 1986, he designed and taught two courses on Reliability Theory. One, which he considered to be fundamental in reliability considerations, was Mathematical Models for Systems Reliability.
Epstein’s lecture notes for Mathematical Models for Systems Reliability have never been published. However, in 1969 they were typed, duplicated and sold to Technion students by the Technion Student Association. Soon enough, they were out of print, but luckily, five copies remained in the library, so students could still use (or copy) them. After Epstein’s retirement and over the last two decades, I taught the course, using Epstein’s notes. During the years, I added some more topics, examples and problems, gave alternative proofs to some results, but the general framework remained Epstein’s.
It is my conviction, that the material presented in this book provides a rigorous treatment of the required probability background for understanding reliability theory. There are many contemporary texts available in the market, which emphasize other aspects of reliability, as statistical methods, life-testing, engineering, reliability of electronic devices, mechanical devices, software reliability, etc.
The book can serve as a text for a one-semester course. It is assumed that the readers of the book have taken courses in Calculus, Linear Algebra and Probability Theory. Knowledge of Statistical Estimation, Differential Equations and Laplace Transform Methods are advantageous, though not necessary, since the basic facts needed are included in the book.Preliminaries
The Poisson process and distribution
Waiting time distributions for a Poisson process
Statistical estimation theory
Generating a Poisson process
Nonhomogeneous Poisson process
Three important discrete distributions
Problems and comments
Statistical life length distributions
Stochastic life length models
Models based on the hazard rate
General remarks on large systems
Problems and comments
Reliability of various arrangements of units
Series and parallel arrangements
Series-parallel and parallel-series systems
Various arrangements of switches
Standby redundancy
Problems and comments
Reliability of a one-unit repairable system
Exponential times to failure and repair
Generalizations
Problems and comments
Reliability of a two-unit repairable system
Steady-state analysis
Time-dependent analysis via Laplace transform
On Model 2(c)
Problems and Comments
Continuous-time Markov chains
The general case
Reliability of three-unit repairable systems
2.1 Steady-state analysis
Steady-state results for the n-unit repairable system
Pure birth and death processes
Some statistical considerations
Problems and comments
First passage time for systems reliability
Two-unit repairable systems
Repairable systems with three (or more) units
Repair time follows a general distribution
Problems and comments
Embedded Markov chains and systems reliability
Computations of steady-state probabilities
Mean first passage times
Problems and comments
Integral equations in reliability theoryExample 1: Renewal process
Example 2: One-unit repairable system
Example 3: Preventive replacements or maintenance
Example 4: Two-unit repairable system
Example 5: One out of n repairable systems
Example 6: Section 7.3 revisited
Example 7: First passage time distribution
Problems and commentsПараметры электронного документа: векторный, структурированный по разделам, 257 с.