Maintenance policy optimization for multi-component systems considering dynamic importance of components

•A novel maintenance policy for a multi-component system is presented.•Multiple dependencies between components are analyzed.•The dynamic importance of components is considered.•The long-run average cost of the system is derived by the semi-regenerative process. A novel maintenance policy for a multi-component system consisting of an auxiliary and a critical component is presented. The deterioration process of the components is described by the Markov process. Multiple dependence between components and the dynamic importance of components are considered. When the auxiliary component degrades to a certain state, it plays a decisive role in system reliability, and then the maintenance decision is made based on the reliability of the auxiliary component. At this time, if the critical component arrives at the state when preventive maintenance (PM) is demanded, it is repaired opportunistically as well as the auxiliary component. The long-run average cost of the system is derived by the technique of the semi-regenerative process. By minimizing the long-run average cost of the system, the optimal inspection period, the PM threshold of the critical component, and the threshold of the auxiliary component are determined. Finally, the effectiveness of the proposed strategy is illustrated by numerical cases.