Statistics Analysis Of Copula Based Bivariate Degradation Model

With the development of science and technology, there appear many highly reliable and long life products. In practical application, the requirements of the product's function become more diversified, and the failure mechanism of high-reliable products becomes more complicated. Thus, many high-reliable products have two or more performance characteristics (PCs), and the PCs may be dependent each other. This paper study the statistical analysis for a bivariate degradation model, which use Wiener process to govern the PC's degradation, and use Copula function to describe the dependence of the PCs. First, IFM method is used to estimate the parameters of the Copula based bivariate degradation model under constant stress. A simulation study is conducted to verify the effectiveness of IFM method comparing with MLE in the real case and under different true value of the Copula parameter. Second, a two-stage method is used to estimate the parameters of the model in CSADT. and an optimal design for CSADT is proposed. Under the constraint that the total experiment cost does not exceed a predetermined budget, the optimal test plan is obtained by minimizing the simulated MSE of the estimated p-percent reliability of the product. An example is illustrated for the proposed method. The influence of the stress level to the optimal test plan is also studied.