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

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