Reliability assessment of interactive competing failure processes under the generalized Pólya shock

In recent years, the competing failure processes gained significant attention as a way of modeling based on degradation and shock processes. A traditional independent competing failure process model assumes that soft failure and hard failure affect the life of the system independently. This modeling method is being improved by a new modeling method, that is, the interaction between soft failure and hard failure affects the life of the system. Therefore, a novel reliability modeling of systems that suffer from mutually dependent competing failure processes under the generalized mixed shock model is proposed. In reliability modeling, the external random shocks can immediately increase the degradation level and degradation rate to accelerate the system degradation. Meanwhile, the internal degradation can continuously change the hard failure threshold to weaken the system strength. Under the above assumptions, analytical expressions for the reliability function for systems under the generalized Pólya process have been derived using the stochastic process theory and probabilistic techniques based on the proposed mixed shock model. Additionally, simulation algorithms to compute the reliability based on the Monte Carlo method are provided. Finally, a case study is verified to illustrate the proposed model and the derived results.