The identifiability problem for repairable systems subject to competing risks

T.J. Bedford, B. Lindqvist

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Within reliability theory, identifiability problems arise through competing risks. If we have a series system of several components, and if that system is replaced or repaired to as good as new on failure, then the different component failures represent competing risks for the system. It is well known that the underlying component failure distributions cannot be estimated from the observable data (failure time and identity of failed component) without nontestable assumptions such as independence. In practice many systems are not subject to the 'as good as new' repair regime. Hence, the objective of this paper is to contrast the identifiability issues arising for different repair regimes. We consider the problem of identifying a model within a given class of probabilistic models for the system. Different models corresponding to different repair strategies are considered: a partial-repair model, where only the failing component is repaired; perfect repair, where all components are as good as new after a failure; and minimal repair, where components are only minimally repaired at failures. We show that on the basis of observing a single socket, the partial-repair model is identifiable, while the perfect- and minimal-repair models are not.
LanguageEnglish
Pages774-790
Number of pages16
JournalAdvances in Applied Probability
Volume36
Issue number3
DOIs
Publication statusPublished - 2004

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Repairable System
Competing Risks
Identifiability
Repair
Minimal Repair
Partial
Failure Time Data
Reliability Theory
Series System
Model
Reliability theory
Probabilistic Model

Keywords

  • reliability
  • marked point process
  • ergodicity
  • markov chain
  • management theory
  • systems analaysis

Cite this

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title = "The identifiability problem for repairable systems subject to competing risks",
abstract = "Within reliability theory, identifiability problems arise through competing risks. If we have a series system of several components, and if that system is replaced or repaired to as good as new on failure, then the different component failures represent competing risks for the system. It is well known that the underlying component failure distributions cannot be estimated from the observable data (failure time and identity of failed component) without nontestable assumptions such as independence. In practice many systems are not subject to the 'as good as new' repair regime. Hence, the objective of this paper is to contrast the identifiability issues arising for different repair regimes. We consider the problem of identifying a model within a given class of probabilistic models for the system. Different models corresponding to different repair strategies are considered: a partial-repair model, where only the failing component is repaired; perfect repair, where all components are as good as new after a failure; and minimal repair, where components are only minimally repaired at failures. We show that on the basis of observing a single socket, the partial-repair model is identifiable, while the perfect- and minimal-repair models are not.",
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The identifiability problem for repairable systems subject to competing risks. / Bedford, T.J.; Lindqvist, B.

In: Advances in Applied Probability, Vol. 36, No. 3, 2004, p. 774-790.

Research output: Contribution to journalArticle

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AU - Lindqvist, B.

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KW - reliability

KW - marked point process

KW - ergodicity

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