Analysis of Type-II progressively hybrid censored data

The mixture of Type-I and Type-II censoring schemes, called the hybrid censoring scheme, is quite common in life-testing or reliability experiments. Recently, Type-II progressive censoring scheme has become quite popular for analyzing highly reliable data. One drawback of the Type-II progressive censoring scheme is that the length of the experiment can be quite large. In this paper, we introduce a Type-II progressively hybrid censoring scheme, where the experiment terminates at a pre-specified time. For this censoring scheme, we analyze the data under the assumptions that the lifetimes of the different items are independent and exponentially distributed random variables with parameter λλ. We obtain the maximum-likelihood estimator of the unknown parameter in an exact form. Asymptotic confidence intervals based on λ^, lnλ^, confidence interval based on likelihood ratio test and two bootstrap confidence intervals are also proposed. Bayes estimate and credible interval of the unknown parameter are obtained under the assumption of gamma prior of the unknown parameter. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.