Comparative Study with Applications for Gompertz Models under Competing Risks and Generalized Hybrid Censoring Schemes

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion.