# Reliability and Maintenance

## Networks and Systems

© 2012 – Chapman and Hall/CRC

344 pages | 95 B/W Illus.

Hardback: 9781439826355
pub: 2012-05-22
US Dollars\$122.95
x

Reliability and Maintenance: Networks and Systems gives an up-to-date presentation of system and network reliability analysis as well as maintenance planning with a focus on applicable models. Balancing theory and practice, it presents state-of-the-art research in key areas of reliability and maintenance theory and includes numerous examples and exercises. Every chapter starts with theoretical foundations and basic models and leads to more sophisticated models and ongoing research.

The first part of the book introduces structural reliability theory for binary coherent systems. Within the framework of these systems, the second part covers network reliability analysis. The third part presents simply structured maintenance policies that may help with the cost-optimal scheduling of preventive maintenance. Each part can be read independently of one another.

Suitable for researchers, practitioners, and graduate students in engineering, operations research, computer science, and applied mathematics, this book offers a thorough guide to the mathematical modeling of reliability and maintenance. It supplies the necessary theoretical and practical details for readers to perform reliability analyses and apply maintenance policies in their organizations.

COHERENT BINARY SYSTEMS

Fundamental System Structures

Simple Systems

Structured Systems

Exercises

Complex Systems

Foundations

Coherent Systems

Exercises

Exercises

NETWORK RELIABILITY

Modeling Network Reliability with Graphs

Introduction to Network Reliability

Foundations of Graph Theory

Deterministic Reliability Measures

Stochastic Reliability Measures

Reliability Analysis

Connectedness

K-Terminal Reliability

Vertex Failures

Residual Connectedness

Directed Graphs

Domination and Covering

Connectedness in Undirected Graphs

The Reliability Polynomial

Special Graphs

Reductions for the K-Terminal Reliability

Inequalities and Reliability Bounds

Partitions of the Vertex Set and Vertex Separators

The Combinatorics of Set Partitions

Separating Vertex Sets — Splitting Formulae

Planar and Symmetric Graphs

Splitting and Recurrent Structures

Approximate Splitting .Reliability Bounds

Reliability Measures Based on Vertex Partitions

Splitting in Directed Graphs

Algorithmic Aspects of Network Reliability

Complexity of Network Reliability Problems

Decomposition-Reduction Algorithms

Algorithms for Special Graph Classes

Simulation and Probabilistic Algorithms

MAINTENANCE MODELS

Random Point Processes in System Replacement

Basic Concepts

Renewal Processes

Minimal Repair Processes

Exercises

Time-Based System Replacement

Age and Block Replacement

Replacement and Minimal Repair

Replacement Policies Based on the Failure Type

Exercises

System Replacement Based on Cost Limits

Introduction

Constant Repair Cost Limit

Time-Dependent Repair Cost Limits

Cumulative Repair Cost Limit Replacement Policies

Exercises

Maintenance Models with General Degree of Repair

Imperfect Repair

Virtual Age

Geometric Time Scaling

Exercises

Inspection of Systems

Basic Problem and Notation

Inspection without Replacement

Inspection with Replacement

Exercises

Bibliography

Index

#### Frank Beichelt

Johannesburg, , Republic of South Africa

Frank Beichelt is a sessional lecturer at the University of Witwatersrand, where he was a professor of operations research before retiring in 2008. He was previously a professor of mathematics at Ingenieurhochschule Mittweida and an associate professor of reliability and maintenance theory at the University for Transportation and Communication "Friedrich List" Dresden. Extensively published in the field of stochastic modeling, Dr. Beichelt has authored nine books and coauthored three books.

Peter Tittmann is a professor of mathematics at the University of Applied Sciences Mittweida. He teaches courses in linear algebra, discrete mathematics, graph theory, operations research, enumerative combinatorics, and network analysis. Dr. Tittman’s research interests include network reliability, graph theory, and combinatorics.