Summary: We present a Bayesian approach to inference in reliability studies based on type II doubly censored data from a Rayleigh distribution. We also consider the problem of predicting an independent future sample from the same distribution in a Bayesian setting. The results can be used to predict the failure-time of a \(k\)-out-of-\(m\) system. Bayes estimators are obtained in nice closed forms. Highest posterior density (HPD) and maximum likelihood (ML) estimators, and HPD intervals can readily be computed using iterative methods.