Epstein / Weissman Mathematical Models for Systems Reliability

1. Auflage 2010
ISBN: 978-1-4200-8083-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 272 Seiten

Evolved from the lectures of a recognized pioneer in developing the theory of reliability, Mathematical Models for Systems Reliability provides a rigorous treatment of the required probability background for understanding reliability theory. This classroom-tested text begins by discussing the Poisson process and its associated probability laws. It then uses a number of stochastic models to provide a framework for life length distributions and presents formal rules for computing the reliability of nonrepairable systems that possess commonly occurring structures. The next two chapters explore the stochastic behavior over time of one- and two-unit repairable systems. After covering general continuous-time Markov chains, pure birth and death processes, and transitions and rates diagrams, the authors consider first passage-time problems in the context of systems reliability. The final chapters show how certain techniques can be applied to a variety of reliability problems. Illustrating the models and methods with a host of examples, this book offers a sound introduction to mathematical probabilistic models and lucidly explores how they are used in systems reliability problems.

Zielgruppe

Graduate students and researchers in mathematics, statistics, and engineering.

Autoren/Hrsg.

Epstein, Benjamin

Weissman, Ishay

Fachgebiete

• Technische Wissenschaften Technik Allgemein Technik: Allgemeines

Inhaltsverzeichnis

Preliminaries

The Poisson process and distribution

Waiting time distributions for a Poisson process

Statistical estimation theory

Generating a Poisson process

Nonhomogeneous Poisson process

Binomial, geometric, and negative binomial distributions

Statistical Life Length Distributions

Stochastic life length models

Models based on the hazard rate

General remarks on large systems

Reliability of Various Arrangements of Units

Series and parallel arrangements

Series-parallel and parallel-series systems

Various arrangements of switches

Standby redundancy

Reliability of a One-Unit Repairable System

Exponential times to failure and repair

Generalizations

Reliability of a Two-Unit Repairable System

Steady-state analysis

Time-dependent analysis via Laplace transform

On model 2(c)

Continuous-Time Markov Chains

The general case

Reliability of three-unit repairable systems

Steady-state results for the n-unit repairable system

Pure birth and death processes

Some statistical considerations

First Passage Time for Systems Reliability

Two-unit repairable systems

Repairable systems with three (or more) units

Repair time follows a general distribution

Embedded Markov Chains and Systems Reliability

Computations of steady-state probabilities

Mean first passage times

Integral Equations in Reliability Theory

Introduction

Example 1: Renewal process with a general distribution

Example 2: One-unit repairable system

Example 3: Effect of 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

References

Index

A Problems and Comments section appears at the end of each chapter.