An optimal condition-based maintenance policy for a degrading system subject to the competing risks of soft and hard failure

• Dependent failure modes and a periodically inspected system are considered.
• The degrading system is described by an age- and state-dependent degradation model.
• A CBM policy with a failure rate-based control limit is proposed.
• An effective computational algorithm in the SMDP framework is developed to optimize the proposed maintenance policy.
• The proposed CBM policy benefits over traditional policies are demonstrated.

The paper considers a maintenance problem in the presence of competing risks (soft and hard failure) for a degrading system subject to condition monitoring at equidistant, discrete time epochs. A random-coefficient autoregressive model with time effect is developed to describe the system degradation. The system age, previous state observations, and the item-to-item variability of the degradation are jointly combined in the proposed degradation model. The failure rate corresponding to the hard failure is characterized by its dependency on the system age and the degradation state. We propose a maintenance policy which initiates preventive maintenance when the failure rate of the hard failure reaches a certain threshold. Computational algorithms for the optimization of the maintenance policy are developed in a semi-Markov decision process framework, with the objective of minimizing the long-run expected average cost. The effectiveness of the proposed method is demonstrated by numerical examples.