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E-raamat: Stochastic Models in Reliability

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This book provides a comprehensive up-to-date presentation of some of the classical areas of reliability, based on a more advanced probabilistic framework using the modern theory of stochastic processes. This framework allows analysts to formulate general failure models, establish formulae for computing various performance measures, as well as determine how to identify optimal replacement policies in complex situations. In this second edition of the book, two major topics have been added to the original version: copula models which are used to study the effect of structural dependencies on the system reliability; and maintenance optimization which highlights delay time models under safety constraints. Terje Aven is Professor of Reliability and Risk Analysis at University of Stavanger, Norway. Uwe Jensen is working as a Professor at the Institute of Applied Mathematics and Statistics of the University of Hohenheim in Stuttgart, Germany. Review of first edition: "This is an excellent book on mathematical, statistical and stochastic models in reliability. The authors have done an excellent job of unifying some of the stochastic models in reliability. The book is a good reference book but may not be suitable as a textbook for students in professional fields such as engineering. This book may be used for graduate level seminar courses for students who have had at least the first course in stochastic processes and some knowledge of reliability mathematics. It should be a good reference book for researchers in reliability mathematics." --Mathematical Reviews (2000)

This book on mathematical, statistical and stochastic models in reliability will help analysts formulate general failure models, establish formulae for computing performance measures, and determine how to identify optimal replacement policies.

Arvustused

 This is an excellent book on mathematical, statistical and stochastic models in reliability. The authors have done an excellent job of unifying some of the stochastic models in reliability. The book is a good reference book but may not be suitable as a textbook for students in professional fields such as engineering.

This book may be used for graduate level seminar courses for students who have had at least the first course in stochastic processes and some knowledge of reliability mathematics. It should be a good reference book for researchers in reliability mathematics.

--Mathematical Reviews

1 Introduction
1(16)
1.1 Lifetime Models
1(6)
1.1.1 Complex Systems
2(1)
1.1.2 Damage Models
3(1)
1.1.3 Different Information Levels
4(1)
1.1.4 Simpson's Paradox
4(1)
1.1.5 Predictable Lifetime
5(1)
1.1.6 A General Failure Model
6(1)
1.2 Maintenance
7(2)
1.2.1 Availability Analysis
8(1)
1.2.2 Optimization Models
9(1)
1.3 Reliability Modeling
9(8)
1.3.1 Nuclear Power Station
11(2)
1.3.2 Gas Compression System
13(4)
2 Basic Reliability Theory
17(40)
2.1 Complex Systems
17(17)
2.1.1 Binary Monotone Systems
17(14)
2.1.2 Multistate Monotone Systems
31(3)
2.2 Basic Notions of Aging
34(8)
2.2.1 Nonparametric Classes of Lifetime Distributions
35(3)
2.2.2 Closure Theorems
38(2)
2.2.3 Stochastic Comparison
40(2)
2.3 Copula Models of Complex Systems in Reliability
42(15)
2.3.1 Introduction to Copula Models
42(3)
2.3.2 The Influence of the Copula on the Lifetime Distribution of the System
45(4)
2.3.3 Archimedean Copulas
49(1)
2.3.4 The Expectation of the Lifetime of a Two-Component-System with Exponential Marginals
50(2)
2.3.5 Marshall-Olkin Distribution
52(5)
3 Stochastic Failure Models
57(48)
3.1 Notation and Fundamentals
57(13)
3.1.1 The Semimartingale Representation
59(9)
3.1.2 Transformations of SSMs
68(2)
3.2 A General Lifetime Model
70(11)
3.2.1 Existence of Failure Rate Processes
72(1)
3.2.2 Failure Rate Processes in Complex Systems
73(4)
3.2.3 Monotone Failure Rate Processes
77(1)
3.2.4 Change of Information Level
78(3)
3.3 Point Processes in Reliability: Failure Time and Repair Models
81(24)
3.3.1 Alternating Renewal Processes: One-Component Systems with Repair
84(1)
3.3.2 Number of System Failures for Monotone Systems
85(1)
3.3.3 Compound Point Process: Shock Models
86(2)
3.3.4 Shock Models with State-Dependent Failure Probability
88(1)
3.3.5 Shock Models with Failures of Threshold Type
89(1)
3.3.6 Minimal Repair Models
90(5)
3.3.7 Comparison of Repair Processes for Different Information Levels
95(2)
3.3.8 Repair Processes with Varying Degrees of Repair
97(1)
3.3.9 Minimal Repairs and Probability of Ruin
98(7)
4 Availability Analysis of Complex Systems
105(70)
4.1 Performance Measures
105(1)
4.2 One-Component Systems
106(14)
4.2.1 Point Availability
108(1)
4.2.2 The Distribution of the Number of System Failures
109(7)
4.2.3 The Distribution of the Downtime in a Time Interval
116(3)
4.2.4 Steady-State Distribution
119(1)
4.3 Point Availability and Mean Number of System Failures
120(5)
4.3.1 Point Availability
120(1)
4.3.2 Mean Number of System Failures
121(4)
4.4 Distribution of the Number of System Failures
125(20)
4.4.1 Asymptotic Analysis for the Time to the First System Failure
126(5)
4.4.2 Some Sufficient Conditions
131(4)
4.4.3 Asymptotic Analysis of the Number of System Failures
135(10)
4.5 Downtime Distribution Given System Failure
145(6)
4.5.1 Parallel System
146(2)
4.5.2 General Monotone System
148(1)
4.5.3 Downtime Distribution of the ith System Failure
149(2)
4.6 Distribution of the System Downtime in an Interval
151(7)
4.6.1 Compound Poisson Process Approximation
152(1)
4.6.2 Asymptotic Analysis
153(5)
4.7 Generalizations and Related Models
158(17)
4.7.1 Multistate Monotone Systems
158(7)
4.7.2 Parallel System with Repair Constraints
165(1)
4.7.3 Standby Systems
166(9)
5 Maintenance Optimization
175(70)
5.1 Basic Replacement Models
175(5)
5.1.1 Age Replacement Policy
175(2)
5.1.2 Block Replacement Policy
177(1)
5.1.3 Comparisons and Generalizations
178(2)
5.2 A General Replacement Model
180(10)
5.2.1 An Optimal Stopping Problem
180(3)
5.2.2 A Related Stopping Problem
183(6)
5.2.3 Different Information Levels
189(1)
5.3 Applications
190(17)
5.3.1 The Generalized Age Replacement Model
190(3)
5.3.2 A Shock Model of Threshold Type
193(1)
5.3.3 Information-Based Replacement of Complex Systems
194(3)
5.3.4 A Parallel System with Two Dependent Components
197(1)
5.3.5 Complete Information About T1, T2 and T
198(4)
5.3.6 A Burn-In Model
202(5)
5.4 Repair Replacement Models
207(8)
5.4.1 Optimal Replacement Under a General Repair Strategy
207(1)
5.4.2 A Markov-Modulated Repair Process: Optimization with Partial Information
208(6)
5.4.3 The Case of m=2 States
214(1)
5.5 Maintenance Optimization Models Under Constraints
215(30)
5.5.1 A Delay Time Model with Safety Constraints
215(14)
5.5.2 Optimal Test Interval for a Monotone Safety System
229(16)
A Background in Probability and Stochastic Processes
245(28)
A.1 Basic Definitions
245(1)
A.2 Random Variables, Conditional Expectations
246(8)
A.2.1 Random Variables and Expectations
246(2)
A.2.2 Lp-Spaces and Conditioning
248(3)
A.2.3 Properties of Conditional Expectations
251(1)
A.2.4 Regular Conditional Probabilities
252(1)
A.2.5 Computation of Conditional Expectations
253(1)
A.3 Stochastic Processes on a Filtered Probability Space
254(3)
A.4 Stopping Times
257(2)
A.5 Martingale Theory
259(7)
A.6 Semimartingales
266(7)
A.6.1 Change of Time
267(1)
A.6.2 Product Rule
268(5)
B Renewal Processes
273(10)
B.1 Basic Theory of Renewal Processes
273(7)
B.2 Renewal Reward Processes
280(1)
B.3 Regenerative Processes
281(1)
B.4 Modified (Delayed) Processes
281(2)
References 283(10)
Index 293