Reliability modeling based on multiple wiener degradation-shock competing failure process and dynamic failure threshold

Given multiple degradation failure and shock failure processes within the complex system during operation, a reliability model that combines the degradation-shock competing failure process and dynamic failure threshold is modeled. The Wiener process with random effects is considered the degradation process model, which includes random effects to account for the heterogeneity among system units. Then, the extreme shock model with a dynamic failure threshold is used to depict the random shock. The copula function is carried out to illustrate the correlation between multiple degradation processes, the reliability model is constructed further. To verify the application of this model, a numerical case and a micro-electro-mechanical system comprising two micro-mechanical resonators are employed. The parameter sensitivity of the proposed model is analyzed. The study results show that the reliability model, which combines the Wiener process with random effects and the dynamic failure threshold, more accurately reflects the actual operational state of the complex system.