Paper Title
Optimal Imperfect Maintenance Policy for A Parallel System with Mission Durations

Abstract
It is well-known that the parallel system, which is one of the most important redundant systems, has usually been designed to achieve high reliability. When a mission arrives at a random time and lasts for a duration for such a system, it is of great importance to make the suitable preventive maintenance during the mission duration.This paper proposes the age replacement policyfor a parallel system with mission durations and imperfect maintenances. The parallel system is subject to two types of failures and implement imperfect maintenance when it has failed, including a minor failure (type I failure), which can be removed by the minimal repair and a catastrophic failure (type II failure), which should be rectified by the corrective replacement.The preventive replacement policy is planned to take place at age T and make the system be reliable for the mission duration.The expected cost rate is obtained theoretically and optimalpreventive replacement ageis derived analytically. Finally, a numerical example is exhibited to demonstrate the effectiveness of the methodology derived in this paper. Keywords - Mission duration, Imperfect maintenance, Parallel system, Optimization, Replacement, Minimal repair.