A Multivariate Correlation Degradation Model for Reliability Analysis Based on Copula

Abstract

Degradation process modeling is an important part of reliability analysis. At present, most researches about it focus on univariate degradation models. The independence assumption is adopted to analyze multivariate degradation indicators. In order to describe the correlation between two or more degradation indicators more accurately, a multivariate correlation degradation model based on copula was proposed to analyze system reliability in this paper. First, the univariate degradation model was established for different degradation process. Then, the cosine similarity measure was used to calculate the overall and local correlations for every two degradation indicators. Combining the cosine similarity values with each copula characteristics, the appropriate copula function was selected to compose Mixed Copula (M-Copula), which could describe the correlation between two degradation indicators well. Based on that, the optimization model with the residual minimization as the objective was constructed and solved to obtain the degradation correlation reliability model. Copula functions with different characteristics are screened by cosine similarity in this method, which could improve the accuracy and efficiency of reliability modeling and life prediction. It could also save cost. Finally, a case was calculated to verify the feasibility and effectiveness.