Group maintenance policies for an R-out-of-N system with phase-type distribution

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This paper presents an extension of our earlier paper on the 1-out-of-N repairable cold standby system (i.e., Barron IIE Trans 47:1139–1151, 2015). Specifically, we consider an R-out-of-N repairable system where the lifetimes of the units follow phase-type distribution. The system is functioning if at least R out of its N components work. Each working component is subject to failure. There are fixed, unit repair, and replacement costs associated with the maintenance facility, which is carried out after a fixed lead time τ. A penalty cost is incurred when the number of good components decreases to R − 1. We assume that the repair takes no time and repaired units are as good as new. By applying renewal theory and matrix-geometric methods, we derive the expected discounted costs under three classes of group maintenance policies: m-failure, T -age, and (m, T,τ), which is a refinement of the classical (m, T) policy. Illustrative examples, a comparative study and insights are provided.

Original languageEnglish
Pages (from-to)79-105
Number of pages27
JournalAnnals of Operations Research
Issue number1-2
StatePublished - Feb 2018


  • Group maintenance
  • Matrix-geometric
  • PH renewal process
  • R-out-of-N system
  • Renewal theory


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