Stocking Repair Kits for Systems with Limited Life

In this paper we examine several models for systems subject to both repairable and nonrepairable failures. A repairable failure can be remedied by the application of a repair kit (spare part, standby system, etc.), whereas a nonrepairable failure terminates the life of the system. The stochastic properties of key system parameters are derived under appropriate assumptions. These results are then used to determine the optimal number of repair kits to stock in order to maintain a system having a specified cost structure. The applicability of such models to problems of systems design is illustrated in several examples. Our results make use of distributions of phase type, and demonstrate that this family of distributions provides considerable flexibility and computational tractability in reliability modeling.