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Optimal Maintenance Design for a Simple Reparable System

This paper discusses an optimal corrective maintenance design for a simple reparable system. The primary interest is to optimize the availability of the system, which is defined as the probability that the system is operating properly when it is requested for use. The system model considered in our current work is governed by coupled transport and integro-differential equations. A corrective maintenance policy is represented by the repair rate, which depends on distributed repair time. The objective is to determine an optimal repair rate that maximizes the availability of the system in good mode over a given system running period. This leads to a bilinear control problem set in a nonreflexive Banach space. A rigorous proof of existence of an optimal controller and the first-order necessary conditions of optimality are presented.