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

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.