A stress-strength model is formulated for s out of k system of identical components. We consider the estimation of system reliability from survival count data from a Bayesian viewpoint. We assume a quadratic loss and a Dirichlet prior distribution. It is shown that a Bayes sequential procedure can be established. The Bayes estimator is compared with the UMVUE obtained by Bhattacharyya and with an estimator based on Mann-Whitney statistic.