Stochastic models in reliability
 Responsibility
 Terje Aven, Uwe Jensen.
 Language
 English.
 Edition
 2nd ed.
 Imprint
 New York : Springer, c2013.
 Physical description
 xiv, 297 p. : ill. ; 25 cm.
 Series
 Stochastic modelling and applied probability 41.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

TA169 .A95 2013  Unknown 
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Creators/Contributors
 Author/Creator
 Aven, Terje.
 Contributor
 Jensen, Uwe, 1931
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction
 Lifetime models
 Complex systems
 Damage models
 Different information levels
 Simpson's paradox
 Predictable lifetime
 A general failure model
 Maintenance
 Availability analysis
 Optimization models
 Reliability modeling
 Nuclear power station
 Gas compression system
 Basic reliability theory
 Complex systems
 Binary monotone systems
 Multistate monotone systems
 Basic notions of aging
 Nonparametric classes of lifetime distributions
 Closure theorems
 Stochastic comparison
 Copula models of complex systems in reliability
 Introduction to copula models
 The influence of the copula on the lifetime distribution of the system
 Archimedean copulas
 The expectation of the lifetime of a twocomponentsystem with exponential marginals
 Marshallolkin distribution
 Stochastic failure models
 Notation and fundamentals
 The semimartingale representation
 Transformations of SSMs
 A general lifetime model
 Existence of failure rate processes
 Failure rate processes in complex systems
 Monotone failure rate processes
 Change of information level
 Point processes in reliability : failure time and repair models
 Alternating renewal processes : onecomponent systems with repair
 Number of system failures for monotone systems
 Compound point process : shock models
 Shock models with statedependent failure probability
 Shock models with failures of threshold type
 Minimal repair models
 Comparison of repair processes for different information levels
 Repair processes with varying degrees of repair
 Minimal repairs and probability of ruin
 Availability analysis of complex systems
 Performance measures
 Onecomponent systems
 Point availability
 The distribution of the number of system failures
 The distribution of the downtime in a time interval
 Steadystate distribution
 Point availability and mean number of system failures
 Point availability
 Mean number of system failures
 Distribution of the number of system failures
 Asymptotic analysis for the time to the first system failure
 Some sufficient conditions
 Asymptotic analysis of the number of system failures
 Downtime distribution given system failure
 Parallel system
 General monotone system
 Downtime distribution of the ith system failure
 Distribution of the system downtime in an interval
 Compound poisson process approximation
 Asymptotic analysis
 Generalizations and related models
 Multistate monotone systems
 Parallel system with repair constraints
 Standby systems
 Maintenance optimization
 Basic replacement models
 Age replacement policy
 Block replacement policy
 Comparisons and generalizations
 A general replacement model
 An optimal stopping problem
 A related stopping problem
 Different information levels
 Applications
 The generalized age replacement model
 A shock model of threshold type
 Informationbased replacement of complex systems
 A parallel system with two dependent components
 Complete information about T1, T2 and T
 A burnin model
 Repair replacement models
 Optimal replacement under a general repair strategy
 A Markovmodulated repair process : optimization with partial information
 The case of m=2 states
 Maintenance optimization models under constraints
 A delay time model with safety constraints
 Optimal test interval for a monotone safety system
 Background in probability and stochastic processes
 Basic definitions
 Random variables, conditional expectations
 Random variables and expectations
 Lpspaces and conditioning
 Properties of conditional expectations
 Regular conditional probabilities
 Computation of conditional expectations
 Stochastic processes on a filtered probability space
 Stopping times
 Martingale theory
 Semimartingales
 Change of time
 Product rule
 Renewal processes
 Basic theory of renewal processes
 Renewal reward processes
 Regenerative processes
 Modified (delayed) processes
 References
 Index.
 Publisher's Summary
 This book provides a comprehensive uptodate 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).
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Subjects
Bibliographic information
 Publication date
 2013
 Series
 Stochastic modelling and applied probability, 01724568 ; 41
 Available in another form
 ( 9781461478942 (online) )
 Available in another form
 ISBN
 9781461478935 (hd.bd.)
 9781461478942 (online)
 1461478936 (hd.bd.)