Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme

Recently, progressive hybrid censoring schemes have become quite popular in a life-testing problem and reliability analysis. However, the limitation of the progressive hybrid censoring scheme is that it cannot be applied when few failures occur before time $T$. In this article, we propose a generalized progressive hybrid censoring scheme, which allows us to observe a pre-specified number of failures. So, the certain number of failures and their survival times are provided all the time. We also derive the exact distribution of the maximum likelihood estimator (MLE) as well as exact confidence interval (CI) for the parameter of the exponential distribution under the generalized progressive hybrid censoring scheme. The results of simulation studies and real-life data analysis are included to illustrate the proposed method.