Repairable systems with dependent components: Stochastic process techniques and models

Ilkka Norros, Pirkko Kuusela, J. Lapuyade-Lahorgue, M. Naldi, M. Sirviö

Research output: Contribution to journalArticleScientificpeer-review

3 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
Number of pages13
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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