Analysis Of Type-II Progressively Hybrid Censored Competing Risks Data

In medical studies or in reliability analysis, it is quite common that the failure of any individual or any item may be attributable to more than one cause. Moreover, the observed data are often censored. Hybrid censoring scheme which is the mixture of conventional Type-I and Type-II censoring schemes is quite useful in life-testing or reliability experiments. Recently Type-II progressive censoring scheme becomes quite popular for analyzing highly reliable data. But in that case the length of the experiment can be quite large. Hence, in this paper we introduce a Type-II progressively hybrid censoring scheme for competing risks data, where the experiment terminates at a pre-specified time. We derive the likelihood inference of the unknown parameters under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. We obtain the maximum likelihood estimators of the unknown parameters in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.