One of the most important problems in the estimation of the parameter of the failure model, is the cost of experimental sampling units, which can be reduced by using any prior information available about ${ heta}$, and devising a two-stage pooling shrunken estimation procedure. We have proposed an estimator of the reliability function (R(t)) of the exponential model using two-stage time censored data when a prior value about the unknown parameter (${ heta}$) is available from the past. To compare the performance of the proposed estimator with the classical estimator, computer intensive calculations for bias, mean squared error, relative efficiency, expected sample size and percentage of the overall sample size saved expressions, were done for varying the constants involved in the proposed estimator (${ ilde{R}}$(t)).