Bivariate preventive maintenance for repairable systems subject to random shocks

Ji Hwan Cha, Maxim Finkelstein, Gregory Levitin

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We consider a bivariate model for preventive maintenance for items operating in a random environment modeled by a Poisson process of shocks. An item is replaced on the predetermined replacement time or on a shock with the predetermined number, whichever comes first. Its failures are minimally repaired in-between. Each shock in our stochastic model has a double effect. First, it acts directly on the failure rate of an item, which results in the corresponding stochastic intensity process. Second, each shock causes additional “damage,” which can be attributed, for example, to a short drop in the output of a system or other adverse consequences. The corresponding bivariate optimization problem is considered and illustrated by detailed numerical examples.

Original languageEnglish
Pages (from-to)643-653
Number of pages11
JournalProceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
Issue number6
StatePublished - 1 Dec 2017

Bibliographical note

Funding Information:
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0093827). The work of the first author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211). The work of the second author was supported by the National research foundation (NRF) of South Africa (Grant No: 103613).

Publisher Copyright:
© 2017, © IMechE 2017.


  • Poisson shock process
  • Preventive maintenance
  • bivariate optimization
  • intensity process
  • minimal repair


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