Optimal bivariate spare ordering policy for a system with imperfect maintenance

Abstract

In this paper, we investigate an ordering-replacement modelling framework for a system deteriorating with two failure types: a repairable failure (Type-I failure) and an unrepairable failure (Type-II failure). Repairable failures are followed by minimal repair, whereas unrepairable failures are removed by a corrective replacement. A spare unit ordered regularly is associated with the system's operation time T and the number N of successive working times for preventive replacement, or ordered in emergency at any unrepairable failure for corrective replacement, whichever is first to happen. Three kinds of objectives – system availability, expected cost rate, and cost-effectiveness – are optimised to seek for the optimal spare unit ordering schedule (T*, N*), respectively. The existence and uniqueness of each optimal ordering policy are derived analytically and computed numerically.