Optimal Bivariate Order-Replacement Policies for a Multi-State Repairable System with Reliability Constraint

Abstract

A bivariate order-replacement policy for a multi-state repairable system with imperfect repair is put forward in this paper, where the decisions on when to order a spare part and when to place a replacement are based on the number of failures. The geometric processes are generalized to depict the characteristics that the successive working times are shorter and shorter while the consecutive repair times are longer and longer. According to the renewal reward theorem, a constrained optimization model for the order-replacement policy is formulated, in which the aim is to minimize the expected long-run cost rate (ELRCR) under the constraint that system availability is not less than a predetermined availability requirement. General representations of the ELRCR and system availability are derived and an approximation result of the optimization model is given under certain assumptions. Illustrative examples are provided to validate the applicability of the proposed order-replacement model and show the advantage of the order-replacement policy for the multi-state repairable system.