Inference of a competing risks model with partially observed failure causes under improved adaptive type-II progressive censoring

In this paper, a competing risks model is analyzed based on improved adaptive type-II progressive censored sample (IAT-II PCS). Two independent competing causes of failures are considered. It is assumed that lifetimes of the competing causes of failure follow exponential distributions with different means. Maximum likelihood estimators (MLEs) for the unknown model parameters are obtained. Using asymptotic normality property of MLE, the asymptotic confidence intervals are constructed. Existence and uniqueness properties of the MLEs are studied. Further, bootstrap confidence intervals are computed. The Bayes estimators are obtained under symmetric and asymmetric loss functions with non-informative and informative priors. For informative priors, independent gamma distributions are considered. Highest posterior density (HPD) credible intervals are obtained. A Monte Carlo simulation study is carried out to compare performance of the established estimates. Furthermore, three different optimality criteria are proposed to obtain the optimal censoring plan. Finally, a real-life data set is considered for illustrative purposes.