In this paper the Rao-Blackwell and Lehmann-Scheff6 theorems are used to derive the minimum variance unbiased estimates of reliability for a number of distributions that have proved useful in life testing. Estimates are also obtained for the case of censored sample in the (one- and two-parameter) exponential case. A result of Pugh comes out as a special case of the gamma and censored one-parameter exponential model and Laurent's result as a special case of the censored twoparameter exponential model.