Estimation of mean life and reliability for exponential life distribution using time censored sample data

The problem of unbiased estimation of the mean life and the reliability for an exponential life distribution using time censored sample data are considered. We prove that there does not exist an unbiased estimator of the mean life based on a time censored sample. On the other hand, for reliability estimation at an arbitrarily specified time point, we give necessary and sufficient conditions for the existence of (i) an unbiased estimator (ii) the uniformly minimum variance unbiased estimator. We also provide a characterization of the class of unbiased estimators of the reliability, based on a sufficient statistic in situations where unbiased estimators exist.