Optimal condition-based maintenance with general repair and two dependent failure modes

Abstract

This paper proposes a condition-based maintenance (CBM) policy for a system subject to dependent soft and hard failures. When the deterioration exceeds a predetermined level, the system experiences a soft failure that can be rectified by corrective general repair or corrective replacement. Three possible actions, namely no maintenance, preventive general repair, and preventive replacement, are considered at each inspection epoch. The hard failure rate depending on both age and deterioration is described by a proportional hazards model with the covariate characterized by a gamma process. The hard failure can be corrected by minimal repair, general repair, or by replacement. Different from previous CBM policies, no thresholds are used to define maintenance actions. The objective is to determine the optimal maintenance policy that minimizes the long-run expected average cost per unit time. The optimization problem is formulated in the semi-Markov decision process (SMDP) framework and solved by the policy iteration algorithm. Two practical numerical examples are provided to illustrate the proposed policy. The comparison with other CBM policies shows an outstanding performance of the proposed policy, as well as the significance of minimal repair and general repair in CBM decision making.