Reliability and Maintenance : Networks and Systems book cover
1st Edition

Reliability and Maintenance
Networks and Systems

ISBN 9781138381988
Published June 7, 2019 by Chapman and Hall/CRC
344 Pages 95 B/W Illustrations

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Book Description

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.

Table of Contents

Fundamental System Structures

Simple Systems
Structured Systems

Complex Systems
Coherent Systems

Lifetime of Coherent Systems
Independent Element Lifetimes
Dependent Element Lifetimes

Modeling Network Reliability with Graphs

Introduction to Network Reliability
Foundations of Graph Theory
Deterministic Reliability Measures
Stochastic Reliability Measures

Reliability Analysis
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

Random Point Processes in System Replacement

Basic Concepts
Renewal Processes
Minimal Repair Processes

Time-Based System Replacement
Age and Block Replacement
Replacement and Minimal Repair
Replacement Policies Based on the Failure Type

System Replacement Based on Cost Limits
Constant Repair Cost Limit
Time-Dependent Repair Cost Limits
Cumulative Repair Cost Limit Replacement Policies

Maintenance Models with General Degree of Repair
Imperfect Repair
Virtual Age
Geometric Time Scaling

Inspection of Systems
Basic Problem and Notation
Inspection without Replacement
Inspection with Replacement



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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.