If  censored samples come  from the same exponential distribution, it is advantageous to pool the samples for estimating the reliability. In practice, when there are censored samples are available and it is uncertain whether these samples come from the same distribution, the question of whether to pool these samples is usually determined via a preliminary test. This is referred to as preliminary test estimation. In this paper, we study the pre-test estimator, the shrinkage estimator and the empirical Bayes shrinkage estimator of the reliability for exponential distributions. Under the uniform prior distribution and the inverted gamma prior distribution the empirical Bayes shrinking estimators are developed and compared with the pre-test estimator and with the shrinkage estimator in terms of mean squared error. An empirical Bayes shrinkage estimator under the inverted gamma prior distribution and Stein's positive rule shrinkage estimator are shown to be preferable when the scale parameters may be similar in size.