Reliability and Maintenance ─ Networks and Systems

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.

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.

COHERENT BINARY SYSTEMSFundamental System Structures Simple Systems Structured SystemsExercises

Complex Systems Foundations Coherent SystemsExercises

Lifetime of Coherent Systems Independent Element Lifetimes Dependent Element LifetimesExercises

NETWORK RELIABILITYModeling Network Reliability with GraphsIntroduction to Network Reliability Foundations of Graph Theory Deterministic Reliability Measures Stochastic Reliability Measures

Reliability AnalysisConnectedness K-Terminal ReliabilityVertex Failures Residual ConnectednessDirected Graphs Domination and Covering

Connectedness in Undirected GraphsThe Reliability PolynomialSpecial GraphsReductions for the K-Terminal Reliability Inequalities and Reliability Bounds

Partitions of the Vertex Set and Vertex SeparatorsThe Combinatorics of Set PartitionsSeparating Vertex Sets — Splitting FormulaePlanar 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 ReliabilityComplexity of Network Reliability Problems Decomposition-Reduction Algorithms Algorithms for Special Graph ClassesSimulation and Probabilistic Algorithms

MAINTENANCE MODELSRandom Point Processes in System Replacement Basic Concepts Renewal Processes Minimal Repair ProcessesExercises

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

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 RepairImperfect Repair Virtual Age Geometric Time Scaling Exercises

Inspection of SystemsBasic Problem and Notation Inspection without ReplacementInspection with ReplacementExercises

Bibliography
Index