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

Ji Hwan Cha, Maxim Finkelstein, Gregory Levitin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

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
Volume34
Issue number8
DOIs
StatePublished - Dec 2018

Keywords

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

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