Reliability analysis for competing failure processes with mutual dependence of the system under the cumulative shock

In this paper, reliability analysis is conducted for a single component system with two dependent competing failure processes, i.e., hard failure induced by external random shock and soft failure caused by continuous degradation process and additional abrupt degradation level due to random shocks. The dependence between the two failure processes is as follows: each random shock causes an additional abrupt increase in the degradation of the system, on the other hand, the total degradation decreases the threshold of the hard failure. Assume that the shock arrives according to a Homogeneous Poisson process, and the continuous degradation of the system follows a linear degradation path. The system fails when the total degradation volume exceeds the soft failure threshold level H, or the accumulated shock damage surpasses the hard failure threshold D(t), whichever occurs first. The reliability function of the system is derived. Finally, a numerical example of Micro-Electro-Mechanical System (MEMS) is provided to illustrate the implementation and effectiveness of the proposed model.