Bayes Analysis of One-Shot Device Testing Data with Dependence Structure Using Copula Models and the Exponential Marginals

In current times, copula models have gained prominence in the realm of lifetime data analysis as a means to explore the interdependence among variables representing lifetime or failure times. A copula, as a multivariate distribution function, employs a dependence parameter to couple the marginal distribution of failure time variables. Its design facilitates the separation of dependence structure from the marginal distributions, a feat unattainable through conventional multivariate distribution functions. This study utilizes three Archimedean copula models with exponential marginals to analyze datasets derived from a one-shot device testing experiment using Bayesian procedures. The Bayesian implementation process entails the utilization of the Metropolis algorithm, while Bayesian model selection tools were employed to compare and evaluate all entertained models. Finally, a real dataset serves as an exemplar to demonstrate the proposed Bayesian methodology.