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

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 $$\tau $$ . 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 ( $$m,T,\tau $$ ), which is a refinement of the classical (m, T) policy. Illustrative examples, a comparative study and insights are provided.