Repairable systems with dependent components: Stochastic process techniques and models

Ilkka Norros, Pirkko Kuusela, Jérôme Lapuyade-Lahorgue, Maurizio Naldi, Mika Sirviö

    Research output: Contribution to journalArticleScientificpeer-review

    5 Citations (Scopus)


    We consider three approaches to the modeling of systems with repairable components by a multivariate stochastic on-off process. First, we discuss the Palm calculus framework for stationary processes and its power in the derivation of general formulae for joint downtime statistics in the case of statistically independent components. Second, a class of Generalized Semi-Markov (GSMP) models is proposed for incorporating both arbitrary component downtime distributions and statistical dependence of component failures. The case of two components is studied in detail. Third, we define the property referred to as weakened-by-failures for a system of repairable components, and prove that it implies association under fairly general conditions. We also give sufficient conditions for our GSMP models to possess this property.
    Original languageEnglish
    Pages (from-to)899-912
    JournalIEEE Transactions on Reliability
    Issue number4
    Publication statusPublished - 2014
    MoE publication typeA1 Journal article-refereed


    • association
    • generalized semi-Markov process
    • weakened by failures


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