On optimal replacement of systems with failure rates described by a random jump process

Ji Hwan Cha, Maxim Finkelstein, Gregory Levitin

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11 Scopus citations


Preventive maintenance (age replacement) of items operating in a random environment modeled by a Poisson shock process, resulting in random jump process in the system failure rate, is considered. The corresponding univariate and bivariate models are described. In the univariate model, an item is replaced either on failure or on the predetermined replacement time, whichever comes first. In the bivariate model, the preventive maintenance is performed also on the occurrence of the mth shock. Each shock in our stochastic model has a triple effect. On one hand, it acts directly on the failure rate of an item, increasing it by a random amount or resulting in a failure. On the other hand, each shock causes additional ‘damage’, which can be attributed, eg, to a short drop in the output of an item. The corresponding optimization problem is formulated and illustrated by detailed numerical examples.

Original languageEnglish
Pages (from-to)1590-1604
Number of pages15
JournalQuality and Reliability Engineering International
Issue number8
StatePublished - Dec 2018

Bibliographical note

Funding Information:
The authors would like to thank the reviewers for helpful comments and careful reading of this paper. 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 NRF grant funded by the Korea government (MSIP) (no. 2016R1A2B2014211). The work of the second author was supported by National Research Foundation (SA) (grant no. 103613).

Publisher Copyright:
© 2018 John Wiley & Sons, Ltd.


  • Poisson process
  • age replacement
  • failure (hazard) rate process
  • preventive maintenance
  • random jump process


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