A Bivariate Maintenance Policy for Multi-State Repairable Systems with Monotone Process

Abstract

In this paper, a sequential failure limit maintenance policy for a repairable system is studied. The system is assumed to have states, including one working state and failure states, and the multiple failure states are classified by, e.g., failure severity or failure cause. The system will be replaced at the th failure and corrective maintenance is conducted immediately at each of the first failures. A reliability-centered preventive maintenance schedule is proposed in which, between two adjacent failures, a preventive maintenance action is taken as soon as the system reliability drops to a critical reliability . Both preventive maintenance and corrective maintenance are assumed to be imperfect. Increasing and decreasing geometric processes are introduced to characterize the efficiency of these two types of maintenance. The objective is to derive an optimal maintenance policy such that the long-run expected cost per unit time is minimized. The explicit expression of the average cost rate is derived, and the corresponding optimal maintenance policy can be determined analytically or numerically. A numerical example is given to illustrate the theoretical results and the procedure. The decision model shows its adaptability to different possible characteristics of the maintained system.