Two shock models for single-component systems subject to mutually dependent failure processes

In this paper, the extreme and delta shock models are studied, in which systems are subject to dependent hard failure and soft failure processes. Under the extreme shock model, a hard failure occurs if the magnitude of a single shock surpasses a critical level, while under the delta shock model, a hard failure occurs if the interval time between two successive shocks is smaller than a threshold. Under both shock models, soft failure of a system happens if the total volume of degradation surpasses a given soft failure threshold. The hard and soft failure processes are interdependent owing to the fact that external shock will bring abrupt increment in the degradation path of the system, and on the other hand, the amount of total degradation will affect the hard failure threshold of the system. The failure of the system occurs if a hard failure or a soft failure occurs, whichever happens first. The reliability expressions of the systems under two shock models are derived explicitly. Some reliability indices of the system are calculated by utilizing the probability analysis method. A case study of the sliding spool is provided to illustrate the proposed model.