Group replacement policies for parallel systems whose components have phase distributed failure times

Consider a system of components operating in parallel. Downtime costs are i ncurred when failed components are not repaired or replaced. There are also fixed, unit repair and replacement costs associated with the system. The f ailure distributions of the components are assumed to be identically distri buted random variables. Results on calculating the expected cost and varian ce per unit time of various group replacement policies will be provided. Co nsideration of variance is important since, in many cases, practitioners wi sh not only to achieve small expected cost but also to reduce variability f rom cycle to cycle. Phase distributions allow for the modeling of a wide ra nge failure time behavior. Closed-form results are derived for the three ma jor classes of group replacement policy (m-failure, T-age, and (m, T)) when the underlying distribution is of phase type.