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El. knyga: Reliability and Maintenance: Networks and Systems

(University of Applied Sciences Mittweida, Germany), (University of Witwatersrand, Johannesburg, South Africa)
  • Formatas: 344 pages
  • Išleidimo metai: 22-May-2012
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781439826362
Kitos knygos pagal šią temą:
Reliability and Maintenance: Networks and SystemsDidesnis paveikslėlis
  • Formatas: 344 pages
  • Išleidimo metai: 22-May-2012
  • Leidėjas: Chapman & Hall/CRC
  • Kalba: eng
  • ISBN-13: 9781439826362
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From the vast literature on mathematical modeling for reliability and maintenance published over the past half century, Beichelt (U. of Witwatersrand, South Africa) and Tittmann (U. of Applied Sciences, Germany) have selected topics they think will interest engineers, computer scientists, operations researchers, and mathematicians both in education and in application. Within sections on coherent binary systems, network reliability, and maintenance models, they consider such topics as complex systems, unconnectedness in undirected graphs, algorithmic aspects of network reliability, system replacement based on cost limits, and inspection of systems. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

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.

Preface xi
I Coherent Binary Systems
1(82)
1 Fundamental System Structures
3(16)
1.1 Simple Systems
3(6)
1.1.1 Basic Concepts
3(2)
1.1.2 Nonparametric Classes of Probability Distributions
5(1)
1.1.3 Parametric Probability Distributions
6(3)
1.2 Structured Systems
9(7)
1.2.1 Introduction
9(1)
1.2.2 Series Systems
9(1)
1.2.3 Redundant Systems
10(6)
1.3 Exercises
16(3)
2 Complex Systems
19(54)
2.1 Foundations
19(3)
2.2 Coherent Systems
22(48)
2.2.1 Definition, Properties and Examples
22(8)
2.2.2 Path-and-Cut Representation of Structure Functions
30(5)
2.2.3 Generation of Disjoint Sum Forms
35(8)
2.2.4 Inclusion--Exclusion, Formations, and Signature
43(5)
2.2.5 Bounds on the System Availability
48(5)
2.2.6 Importance Criteria
53(16)
2.2.7 Modular Decomposition
69(1)
2.3 Exercises
70(3)
3 Lifetime of Coherent Systems
73(10)
3.1 Independent Element Lifetimes
73(2)
3.2 Dependent Element Lifetimes
75(6)
3.2.1 Introduction
75(1)
3.2.2 Positive Quadrant Dependence
76(2)
3.2.3 Bivariate PQD Probability Distributions
78(3)
3.3 Exercises
81(2)
II Network Reliability
83(138)
4 Modeling Network Reliability with Graphs
85(14)
4.1 Introduction to Network Reliability
85(2)
4.2 Foundations of Graph Theory
87(4)
4.2.1 Undirected Graphs
87(3)
4.2.2 Directed Graphs
90(1)
4.3 Deterministic Reliability Measures
91(4)
4.4 Stochastic Reliability Measures
95(4)
5 Reliability Analysis
99(36)
5.1 Connectedness
99(3)
5.2 K-Terminal Reliability
102(4)
5.2.1 Some Basic Inequalities for the K-Terminal Reliability
103(3)
5.3 Vertex Failures
106(1)
5.4 Residual Connectedness
107(8)
5.4.1 Vertex Connectivity Polynomial
107(4)
5.4.2 Residual Network Reliability
111(4)
5.5 Directed Graphs
115(8)
5.5.1 Algebraic Methods for Digraphs
118(5)
5.6 Domination and Covering
123(12)
5.6.1 Domination Reliability
124(7)
5.6.2 Vertex Coverings
131(4)
6 Connectedness in Undirected Graphs
135(30)
6.1 Reliability Polynomials
135(9)
6.1.1 Representations of the Reliability Polynomial
136(2)
6.1.2 Reliability Functions
138(2)
6.1.3 Inclusion--Exclusion and Domination
140(2)
6.1.4 Combinatorial Properties of the Reliability Polynomial
142(2)
6.2 Special Graphs
144(6)
6.2.1 Complete Graphs
144(3)
6.2.2 Recurrent Structures
147(3)
6.3 Reductions for the K-Terminal Reliability
150(10)
6.3.1 Simple Reductions
151(2)
6.3.2 Polygon-to-Chain Reductions
153(4)
6.3.3 Delta--Star and Star--Delta Transformations
157(3)
6.4 Inequalities and Reliability Bounds
160(5)
7 Partitions of the Vertex Set and Vertex Separators
165(30)
7.1 Combinatorics of Set Partitions
165(4)
7.1.1 Connected Partitions
166(2)
7.1.2 Incidence Functions
168(1)
7.2 Separating Vertex Sets --- Splitting Formulae
169(9)
7.2.1 All-Terminal Reliability
169(3)
7.2.2 K-Terminal Reliability
172(2)
7.2.3 Splitting and Reduction
174(4)
7.3 Planar and Symmetric Graphs
178(2)
7.4 Splitting and Recurrent Structures
180(2)
7.5 Approximate Splitting --- Reliability Bounds
182(4)
7.6 Reliability Measures Based on Vertex Partitions
186(4)
7.7 Splitting in Directed Graphs
190(5)
8 Algorithmic Aspects of Network Reliability
195(26)
8.1 Complexity of Network Reliability Problems
196(1)
8.2 Decomposition--Reduction Algorithms
197(3)
8.3 Algorithms for Special Graph Classes
200(15)
8.3.1 Graphs of Bounded Tree-Width
200(10)
8.3.2 Domination Reliability of Cographs
210(2)
8.3.3 Graphs of Bounded Clique-Width
212(3)
8.4 Simulation and Probabilistic Algorithms
215(6)
8.4.1 Testing of States
215(1)
8.4.2 Basic Monte Carlo Sampling
216(1)
8.4.3 Refined Sampling Methods
217(4)
III Maintenance Models
221(80)
9 Random Point Processes in System Replacement
223(22)
9.1 Basic Concepts
223(3)
9.2 Renewal Processes
226(11)
9.2.1 Renewal Function
226(5)
9.2.2 Alternating Renewal Processes
231(3)
9.2.3 Compound Renewal Processes
234(3)
9.3 Minimal Repair Processes
237(5)
9.3.1 Pure Minimal Repair Policy and Nonhomogeneous Poisson Processes
237(2)
9.3.2 Minimal Repair Process with Embedded Renewals
239(3)
9.4 Exercises
242(3)
10 Time-Based System Replacement
245(12)
10.1 Age and Block Replacement
246(3)
10.2 Replacement and Minimal Repair
249(2)
10.3 Replacement Policies Based on the Failure Type
251(4)
10.4 Exercises
255(2)
11 System Replacement Based on Cost Limits
257(16)
11.1 Introduction
257(1)
11.2 Constant Repair Cost Limit
258(3)
11.3 Time-Dependent Repair Cost Limits
261(4)
11.4 Cumulative Repair Cost Limit Replacement Policies
265(7)
11.5 Exercises
272(1)
12 Maintenance Models with General Degree of Repair
273(12)
12.1 Imperfect Repair
273(3)
12.2 Virtual Age
276(4)
12.3 Geometric Time Scaling
280(4)
12.4 Exercises
284(1)
13 Inspection of Systems
285(16)
13.1 Basic Problem and Notation
285(1)
13.2 Inspection without Replacement
286(8)
13.2.1 Known Lifetime Distribution
286(4)
13.2.2 Unknown Lifetime Distribution
290(2)
13.2.3 Partially Known Lifetime Distribution
292(2)
13.3 Inspection with Replacement
294(4)
13.3.1 Basic Model
294(2)
13.3.2 Maximum Availability under Cost Restrictions
296(2)
13.4 Exercises
298(3)
Bibliography 301(24)
List of Symbols 325(2)
Index 327
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. Tittmans research interests include network reliability, graph theory, and combinatorics.
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