Reliability modeling for dependent competing failure processes with mutually dependent degradation process and shock process

Many systems experience dependent competing failure processes resulting from simultaneous exposure to degradation processes and random shocks. Moreover, the degradation process and shock process may be mutually dependent. On the one hand, shocks can cause sudden degradation increments, which accelerate degradation process. On the other hand, the occurrence intensity of shock process will increase with the accumulation of degradation. Due to the mutual dependence between degradation and random shocks, the arrival shocks can cause abrupt degradation and then facilitate the occurrence of random shocks recursively. Therefore, the intensity is dependent on the number of arrival shocks, and the shock process cannot be described by the Poisson process used in previous studies. In this paper, a Facilitation model, which is a special type of Markov point process, is introduced to model the shock process. Furthermore, based on the Facilitation model, a novel analytical reliability model with the mutual dependence is developed. A case of a jet pipe servo valve is presented to demonstrate the developed model. The result showed that the reliability declines significantly when considering the mutual dependence.