1st Edition

Reliability and Maintenance Networks and Systems

By Frank Beichelt, Peter Tittmann Copyright 2012
    344 Pages 95 B/W Illustrations
    by Chapman & Hall

    344 Pages 95 B/W Illustrations
    by Chapman & Hall

    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

    Lifetime of Coherent Systems
    Independent Element Lifetimes
    Dependent Element Lifetimes
    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

    Biography

    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.