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

Yonit Barron ()
Yonit Barron: Ariel University

Annals of Operations Research, 2018, vol. 261, issue 1, No 3, 79-105

Abstract: Abstract 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 $$\tau$$ τ . A penalty cost is incurred when the number of good components decreases to $$R-1$$ 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 ( $$m,T,\tau$$ m , T , τ ), which is a refinement of the classical (m, T) policy. Illustrative examples, a comparative study and insights are provided.

Keywords: R-out-of-N system; Group maintenance; Renewal theory; Matrix-geometric; PH renewal process (search for similar items in EconPapers)
Date: 2018
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