New failure and minimal repair processes for repairable systems in a random environment

Ji Hwan Cha, Maxim Finkelstein

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Most often, minimal repair is defined as a replacement of a failed item by an operable item that has the same distribution of the remaining lifetime as the failed one just prior a failure. This is the so-called statistical minimal repair extensively explored in the literature. Another well-known type of minimal repair takes into account the state of a system prior to a failure (the information-based minimal repair). In this paper, we suggest the new type of minimal repair to be called conditional statistical minimal repair. Our approach goes further and deals with the corresponding minimal repair processes for systems operating in a random environment. Moreover, we also consider heterogeneous populations of items, which makes the model more realistic. Both of these aspects that affect the failure mechanism of items are studied. Environment is modeled by the nonhomogeneous Poisson shock process. Two models for the failure mechanism defined by the extreme shock model and the cumulative shock model, respectively, are considered. Some examples illustrating our findings are presented.

Original languageEnglish
Pages (from-to)522-536
Number of pages15
JournalApplied Stochastic Models in Business and Industry
Issue number3
StatePublished - 1 May 2019


  • cumulative shock model
  • extreme shock model
  • information-based minimal repair
  • nonhomogeneous poisson process
  • random environment
  • statistical minimal repair


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