This paper deals with the estimation of the parameter of the Rayleigh distribution with the probability density function and the reliability function, respectively, given by \[ f(x\,|\,\theta)=(x/\theta^2)\exp\left\{-{x^2/2\theta^2}\right\}, \;x>0,\;\text{and}\;R(x\,|\,\theta)=\exp\left\{-{x^2/2\theta^2}\right\},\;x>0, \] where \(\theta>0\) is a parameter. Bayes estimators and highest posterior density credible intervals for the parameter \(\theta\) and the reliability function \(R(x\,|\,\theta)\) of the Rayleigh distribution, as well as the Bayes predictive estimator and the prediction interval for future observations, are obtained based on progressively type II censored samples. In the Bayesian approach considered in this paper, \(\theta\) is a random variable having a conjugate prior distribution of the form
\[ \Pi(\theta)=a^{b}(\Gamma(b)2^{b-1})^{-1}\theta^{-2b-1}\exp\left\{-{a/2\theta^2}\right\},\;\theta>0,\text{ where }a>0, b>0. \]
Two numerical examples are presented for illustration and simulation study.