Bayesian inference on reliability parameter with non-identical-component strengths for Rayleigh distribution

In this paper, we delve into Bayesian inference related to multi-component stress-strength parameters, focusing on non-identical component strengths within a two-parameter Rayleigh distribution under the progressive first failure censoring scheme. We explore various scenarios: the general case, and instances where the common location parameter is either unknown or known. For each scenario, point and interval estimates are derived using methods including the MCMC method, Lindley's approximation, exact Bayes estimates, and HPD credible intervals. The efficacy of these methods is evaluated using a Monte Carlo simulation, and their practical applications are demonstrated with a real data set.