Condition-based maintenance with dynamic thresholds for a system using the proportional hazards model

The hazard rate of many practical systems depends not only on age but also on a diagnostic covariate process. Effective maintenance decisions for such systems need to combine both age information and the covariate information obtained from condition monitoring. This paper proposes a condition-based maintenance (CBM) policy with dynamic thresholds and multiple maintenance actions for such a system subject to periodic inspection. The hazard rate is described by the proportional hazards model with a continuous-state covariate process. At each inspection epoch, appropriate action is selected from no maintenance, imperfect maintenance, and preventive replacement based on two dynamic thresholds. Over an inspection interval, the system may experience minor failure or catastrophic failure that can be addressed by minimal repair and corrective replacement, respectively. The objective is to determine the optimal thresholds that minimize the long-run average cost rate. A modified policy-iteration algorithm is developed to solve the optimization problem in the semi-Markov decision process (SMDP) framework. The effectiveness of the proposed approach is illustrated by a practical numerical example. The comparison with the other CBM policies confirms the outstanding performance of the proposed policy.