Modeling zoned shock effects on stochastic degradation in dependent failure processes

This article studies a system that experiences two dependent competing failure processes, in which shocks are categorized into different shock zones. These two failure processes, a stochastic degradation process and a random shock process, are dependent because arriving shocks can cause instantaneous damage on the degradation process. In existing studies, every shock causes an abrupt damage on degradation. However, this may not be the case when shock loads are small and within the tolerance of system resistance. In the proposed model, only shock loads that are larger than a certain level are considered to cause abrupt damage on degradation, which makes this new model realistic and challenging. Shocks are divided into three zones based on their magnitudes: safety zone, damage zone, and fatal zone. The abrupt damage is modeled using an explicit function of shock load exceedances (differences between load magnitudes and a given threshold). Due to the complexity in modeling these two dependent stochastic failure processes, no closed form of the reliability function can be derived. Monte Carlo importance sampling is used to estimate the system reliability. Finally, two application examples with sensitivity analyses are presented to demonstrate the models.