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

Consider a system of components operating in parallel. Downtime costs are incurred when failed components are not repaired or replaced. There are also fixed, unit repair and replacement costs associated with the system. The failure distributions of the components are assumed to be identically distributed random variables. Results on calculating the expected cost and variance per unit time of various group replacement policies will be provided. Consideration of variance is important since, in many cases, practitioners wish not only to achieve small expected cost but also to reduce variability from cycle to cycle. Phase distributions allow for the modeling of a wide range failure time behavior. Closed-form results are derived for the three major classes of group replacement policy (m-failure, T-age, and (m, T)) when the underlying distribution is of phase type.