Group replacement policies for a repairable cold standby system with fixed lead times

Consider a multi-component repairable cold standby system and assume that repaired units are as good as new. The operational times of the units follow phase-type distribution. Downtime cost is occurred when failed components are not repaired or replaced. There are also fixed, unit repair, and replacement costs associated with the maintenance facility, which are carried out after a fixed lead time τ. Closed-form results are derived for three classes of group replacement policies (m-failure, T-age, and (m, T, τ), which is a refinement of the classic (m, T) policy) for the expected discounted case and for the long-run average criteria. Illustrative examples are provided.