Analysis of multivariate dependent accelerated degradation data using a random-effect general Wiener process and D-vine Copula

A modern product usually shows multiple performance characteristics that degrade simultaneously. It is quite common that these degradation processes are dependent due to some common factors such as internal structure, operating conditions, and working history. Technically, the essence of modeling such dependent degradation processes is to find appropriate marginal degradation models and capture the dependence structure among the multiple performance characteristics. This paper develops a multivariate dependent accelerated degradation test model based on a random-effect general Wiener process and D-vine copula. The proposed model and statistical inference method analyze nonlinear accelerated degradation data considering three sources of uncertainty and construct the marginal distributions. To overcome the lack of flexibility and parameter restrictions of standard multivariate copulas, the pair-copula constructions and their vine graphical representations are applied to reveal and fully understand the complex and hidden dependence patterns in the multivariate degradation data. A simulation example and a real application on the accelerated degradation data of a tuner are provided to illustrate the performance and benefits of the proposed model and statistical estimation method.