Copula for Dependent Competing Risks Model in Progressive‐Stress Accelerated Life Tests

ABSTRACT In the competing risks' model, there are more than one failure causes, and each cause possibly leads to the final failure of the unit. The unit operation may cause correlation among the failure causes. So, a failure cause is commonly associated with the other failure causes, and it is not usually possible to study the units with the independent failure cause, and it is necessary to access each failure cause in the presence of other failure causes. This limitation is rectified by dependent competing risk models, resulting in better predictions of competing events and better decisions. In this paper, we focus on a dependent competing risk model where the units lifetimes follow a Gompertz distribution. Data were obtained from progressive‐stress accelerated life tests under a Type‐II progressive censoring scheme. The dependence structure was modeled using the Gumbel copula. We estimated model parameters using maximum likelihood, percentile, Anderson‐Darling, and Bayesian approaches. Both point and interval estimates were constructed, with bootstrap confidence intervals and highest posterior density credible intervals. The Metropolis–Hastings algorithm was employed for Bayesian estimation. To illustrate the model and the efficiency of the proposed methods, we conducted numerical simulations and analyzed a real‐world dataset.