The paper provides a Bayesian shrinkage method of estimating reliability of series system with identical exponential distribution of failure times. Data are available from Type II censored samples. The Bayesian shrinkage estimator of the scale parameter of the exponential distribution is also obtained using inverted gamma prior. If is the prior or guess value of a parameter , the ordinary shrunken estimator proposed by Thompson (1968), with K a constant , is more efficient than the unbiased estimator if is close to and less efficient otherwise. Here we postulate a prior distribution of around and use an ordinary Bayes estimator instead of in . The Bayesian shrinkage estimators of the scale parameter and reliability function of the series system have thus been obtained and Monte-Carlo study of their efficiencies with respect to unbiased and maximum likelihood estimators revealed that the proposed estimators are better.