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Stochastic models in reliability / Terje Aven, Uwe Jensen.

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Author/Creator:
Aven, Terje.
Language:
English.
Publication date:
2013
Imprint:
2nd ed. - New York : Springer, c2013.
Format:
  • Book
  • xiv, 297 p. : ill. ; 25 cm.
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 two-component-system with exponential marginals
  • Marshall-olkin 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 : one-component systems with repair
  • Number of system failures for monotone systems
  • Compound point process : shock models
  • Shock models with state-dependent 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
  • One-component systems
  • Point availability
  • The distribution of the number of system failures
  • The distribution of the downtime in a time interval
  • Steady-state 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
  • Information-based replacement of complex systems
  • A parallel system with two dependent components
  • Complete information about T1, T2 and T
  • A burn-in model
  • Repair replacement models
  • Optimal replacement under a general repair strategy
  • A Markov-modulated 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
  • Lp-spaces 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.
Contributor:
Jensen, Uwe, 1931-
Available in another form:
9781461478942 (online)
(GyWOH)har135018735
Series:
Stochastic modelling and applied probability, 0172-4568 ; 41
Stochastic modelling and applied probability 41.
Subjects:
ISBN:
9781461478935
1461478936

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