Statistical inference for a Copula-based simple step-stress accelerated life model

In this paper, we undertake a statistical analysis of a simple step-stress accelerated competing failure model. The prevailing hypothesis posits that the competing failure modes are mutually independent. However, empirical evidence suggests that failures tend to be dependent in practice. Consequently, we hypothesize that the failure mechanisms are interconnected. The dependence structure examined in this article is constructed by Gumbel-Hougard Copula and Clayton Copula, and different construction methods are compared. The estimation of unknown parameters is achieved through the maximum likelihood estimation method. The precision of these estimates is subsequently evaluated through Monte Carlo simulations. The simulation results demonstrate that: The Copula theory plays a monumental role in the study of the correlation of competitive failure mechanisms. In this regard, the Gumbel-Hougard Copula demonstrates superior performance in comparison to the Bivariate Clayton Copula within the same framework. Finally, the methods of inference discussed are illustrated with a real dataset.