Optimal rearrangement and preventive maintenance policies for heterogeneous balanced systems with three failure modes

Abstract

This paper studies a heterogeneous balanced system composed of multiple interchangeable components. The degradation process of components is described by a gamma process, and deterioration rates in different positions are different due to the effect of loading stress or temperature. Three competing failures may occur: a) shock failure caused by environment shocks, b) soft failure when the deterioration level of any component exceeds a critical value, and c) out of balance when the difference value among components reaches the failure threshold. To avoid system failure, a rearrangement action is adopted to change the position of components. Besides, preventive maintenance is considered when a component deteriorates severely. A semi-Markov decision process (SMDP) is developed to obtain the optimal policy by minimizing the average maintenance cost. To facilitate calculation, the data transmission method is used to convert the semi-Markov decision model to the Markov decision model, and a value iteration algorithm is established to obtain the optimal maintenance action at each state. Considering practical implications, an imperfect preventive and opportunistic maintenance model is formulated under the SMDP framework. Finally, a typical tire rotation problem in motorcycles proves that the imperfect maintenance policy outperforms the other policies when replacement fees are more expensive.