Optimal Maintenance Policy for Deteriorating Systems Subject to External Shock Damage Under a Semi-Markov Decision Process

Abstract

Condition-based maintenance of systems that deteriorates in accordance with a semi-Markov process was investigated. In addition to considering the system deterioration state as a criterion for maintenance decisionmaking, the cumulative damage caused by random external shocks was considered as well. The occurrence of random shocks was assumed to follow a Poisson process. Furthermore, the damage from random external shocks was assumed to be affected by the system deterioration state, and the system deterioration process was assumed to be affected by the cumulative damage from random external shocks. The system operator chooses the maintenance actions (continue to operate, repair, or replace) that minimize the total expected discounted cost over an infinite time horizon at the time when the system deterioration state changes. The maintenance policy optimization problem is formulated as a semi-Markov decision process considering cumulative damage from random external shocks. The properties of the total expected discounted cost with respect to the system deterioration state and cumulative damage are proven to be monotone. A threshold-type maintenance policy is derived on the basis of the monotone properties. Numerical examples illustrate the threshold-type maintenance policy.