On the Replenishment of Repair Kit Inventories for Systems with Life Distributions of Phase Type

Several models are developed for the evaluation of replenishment policies for an inventory of repair kits used by a system subject to both repairable and nonrepairable failures. At the time of a repairable failure, a repair kit is removed from inventory and used to renew the system. Nonrepairable failures are assumed to occur at some time in the future distributed as a random variable of phase type and permanently terminate the life of the system. Under general stochastic assumptions concerning the lifetime of the components and the time required to perform repair, reorder strategies are identified which maximize the expected net discounted contribution over the lifetime of the systems.