In this article, we have assumed that the observations are carried out for a period of time T, and when a unit failed, it was replaced with a new identical unit. We have considered the exponential distribution of failure, and we have proposed two estimators of reliability function (R(t)) by using time-censored data when a prior value (uncertain prior information) about the unknown parameter (u) was previously available. The expressions for the bias, risk and relative efficiency were obtained. The investigation concerning the improvement of the proposed estimators of R(t) on the bases of the criterion of bias ratio, risk and relative efficiency under different cases showed that the proposed estimators were better than the classical estimators. The conclusions, concluding remarks and limitations were then reported.