Condition-based maintenance for a balanced system considering dependent soft and hard failures

Maintenance optimization for balanced systems has received increasing attention for its significance in engineering practice. Most existing maintenance models for balanced systems consider a single failure mode, which is inconsistent with many practical situations involving multiple failure modes. This paper investigates the maintenance optimization problem for a balanced system that consists of two balanced components and a core component. The balanced components deteriorate during operation and a soft failure occurs if one of their deterioration levels exceeds a critical level. The core component is subject to hard failure and the failure rate depends on its age and the balance condition quantified by the deterioration difference between balanced components. Corrective replacement is performed for soft or hard failure, whichever occurs first. If no failure occurs before a decision epoch, one in three actions, including do-nothing, preventive repair, and preventive replacement, should be chosen based on the information of age and deterioration The objective is to determine the optimal maintenance policy that minimizes the long-run average cost rate. The optimization problem is formulated in the semi-Markov decision process (SMDP) framework. A recursive method is employed to assess conditional reliability. A policy-iteration algorithm is developed to obtain the optimal policy. Results from a numerical example confirm the effectiveness of the proposed approach.