Cooperative Predictive Maintenance of Repairable Systems With Dependent Failure Modes and Resource Constraint

Abstract

Many works on condition-based maintenance of repairable systems apply to either a single failure mode, or statistically independent failure modes. Different from these works, this paper considers the problem of predictive maintenance of repairable systems with dependent failure modes, and resource constraints. Assume that (i) a repairable system is subject to two statistically dependent failure modes bidirectionally affecting each other, (ii) imperfect maintenance actions are cooperatively performed on two dependent failure modes by allocating insufficient resources spent for maintenance, and (iii) future maintenance scheduled at the current time depend on both the predicted number of future failures and the minimization of the expected maintenance cost rate defined in the long term. To resolve the above problem, a novel cooperative predictive maintenance model is proposed. Its basis is the incorporation of the hazard-rate function, and effective age. In this model, two failure modes are statistically dependent in such a way that the hazard rate of one failure mode depends on the accumulated number of failures of the other failure mode. The effect of imperfect maintenance is interpreted in terms of how the hazard rate function and the effective age are changed by maintenance actions. The age reduction factor for each failure mode due to maintenance has some deterministic relation to the degree of resources cooperatively allocated to perform maintenance. The decision variables in the maintenance policy, namely the number of maintenance actions to be performed, the interval between successive maintenance actions, and the cooperatively allocated degree of resources, can be recursively updated when new monitored information arrives. This approach relies on both the predicted number of future failures, and the minimization of the expected maintenance cost rate defined in the long term.