Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 13 2 2024 08 01 Bayesian inference on reliability parameter with non-identical-component strengths for Rayleigh distribution 33 52 3952 10.22103/jmmr.2023.21854.1471 EN Akram Kohansal Department of Statistics, Imam Khomeini International University, Qazvin, Iran. Journal Article 2023 07 10 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. Multi-component stress-strength reliability Lindley's approximation MCMC method First failure progressive censored https://jmmrc.uk.ac.ir/article_3952_a44afea3d9f0c62e0d330071c93de6ee.pdf