Inference for accelerated bivariate dependent competing risks model based on Archimedean copulas under progressive censoring

Dependent competing risks model is a practical model in the analysis of lifetime and failure modes. The dependence can be captured using a statistical tool to explore the relationship among failure causes. In this paper, an Archimedean copula is chosen to describe the dependence in a constant-stress accelerated life test. We study the Archimedean copula based dependent competing risks model using parametric and nonparametric methods. The parametric likelihood inference is presented by deriving the general expression of likelihood function based on assumed survival Archimedean copula associated with the model parameter estimation. Combining the nonparametric estimation with progressive censoring and the nonparametric copula estimation, we introduce a nonparametric reliability estimation method given competing risks data. A simulation study and a real data analysis are conducted to show the performance of the estimation methods.