Many mechanical systems are subject to degradation and random shock processes, which are dependent and competing. The two processes are soft failure process and hard failure process, either of which occurs will cause the system to fail. In this paper, a hard failure model of the gear system is established based on the Stress-Strength Interference model, and a soft failure model of the system is also proposed. To consider the dependence between the two failure processes, the copula function is adopted. Then, the reliability model of the system subject to degradation and shocks is developed, and an expression of the system reliability is derived. Finally, a planetary gear transmission system is taken as a numerical example to demonstrate the effectiveness of the proposed model, which is considered a k-out-of-n system experiencing the processes of degradation and random shocks. Moreover, the effect of model parameters on reliability is evaluated through sensitivity analysis.

In this paper, a system reliability model subject to Dependent Competing Failure Processes (DCFP) with phase-type (PH) distribution considering changing degradation rate is proposed. When the sum of continuous degradation and sudden degradation exceeds the soft failure threshold, soft failure occurs. The interarrival time between two successive shocks and total number of shocks before hard failure occurring follow the continuous PH distribution and discrete PH distribution, respectively. The hard failure reliability is calculated using the PH distribution survival function. Due to the shock on soft failure process, the degradation rate of soft failure will increase. When the number of shocks reaches a specific value, degradation rate changes. The hard failure is calculated by the extreme shock model, cumulative shock model, and run shock model, respectively. The closed-form reliability function is derived combining with the hard and soft failure reliability model. Finally, a Micro-Electro-Mechanical System (MEMS) demonstrates the effectiveness of the proposed model.

In this paper, a novel multistage reliability model is provided as systems are often divided into many stages according to system degradation characteristics. Multistage hard failure (caused by random shock) process (MHFP) and multistage soft failure (caused by random shock and continuous degradation) process (MSFP) are introduced to describe the competing failure processes, where either the MSFP or MHFP would break down the system. The shock processes impact the system in three ways: (1) fatal load shocks cause hard failure immediately in the hard failure process; (2) time shocks cause a hard failure threshold changing;(3) damage load shocks cause degradation level increasing in the soft failure process. In this paper, a density function dispersion method is carried out to address the multistage reliability model, and the effectiveness of the proposed models is demonstrated by reliability analysis with the one-stage model. Finally, the multistage model is applied to a case study, the degradation process is divided into three stages, and the hard failure threshold can be transmitted twice. The proposed model can be applied in other multistage situations, and the calculation method can satisfy the accuracy requirements.