An Age- and State-Dependent Competing Failure Process Model With Wiener Process and Different Failure Threshold Case

This study aims to develop some novel dependent competing failure processes (DCFP) model subject to the degradation failure process and shock failure process. Those two failure processes are dependent due to three forms of correlation: first, each shock load results in additional sudden degradation; second, there exist bidirectional interactions between natural degradation and random shock; and third, the present state exerts an influence on the failure threshold. Firstly, a DCFP model is obtained, where the soft failure is described by a Wiener process, and hard failure is caused by random shock. Furthermore, when the bidirectional effects are considered, some novel DCFP models are established. At last, some new system reliability models are obtained under the different random failure threshold situations. A real numerical example about MEMS oscillator is conducted to explain the given model and procedure. Numerical results demonstrate that random shocks, random failure thresholds, and bidirectional effects all have significantly impact on the system reliability. Furthermore, some sensitivity analysis results are provided.