A shock model for multi-component system considering the cumulative effect of severely damaged components

In this paper, a new shock model for multi-component system combining the cumulative effect of severely damaged components with individual component failure is proposed. It is motivated by the battery pack in an electric vehicle, where some severely damaged cells usually have crucial impacts on the performance of the whole battery pack. In the new model, we introduce a definition of target component to represent such severely damaged components. The proposed system works in a shock environment and has two failure criteria. First, the system fails if at least one component fails. Besides, the system also breaks down when the total number of damaging shocks that some target components have suffered reaches a predetermined critical value. The overlapping finite Markov chain imbedding approach is proposed for the first time to derive system reliability and expected shock length. An integrated maintenance policy is designed for a special case where the time intervals between any two consecutive shocks follow a continuous phase-type distribution, and a corresponding optimization model is established to obtain the optimal inspection time. Several numerical examples for battery packs in electric vehicles are calculated to illustrate the proposed shock model and maintenance policy. This study is of reference value and application significance for similar multi-component systems.