The present article discusses a stress–strength model of the form \(\eta = P[T< U < V]\) , where \(T\) , \(U\) , and \(V\) are independent Rayleigh-distributed random variables. Under this setup, the classical and Bayesian estimation of \(\eta \) has been presented for progressive first failure censored data. In classical point estimation, in addition to the maximum likelihood estimator of \(\eta \) , the maximum product spacings estimator of \(\eta \) under progressive first failure censored data is developed for the first time in the literature. Further, assuming Jeffrey’s and independent conjugate gamma priors for the unknown parameters, the Bayes estimator of \(\eta \) under a symmetric loss function is developed through Markov chain Monte Carlo (MCMC) and Lindley’s approximation. In interval estimation, we have developed asymptotic confidence intervals using maximum likelihood and maximum product spacing estimates. Moreover, Bayesian confidence intervals with Jeffrey’s and gamma priors are also obtained. An empirical study has been conducted to examine the behavior of various point and interval estimators. The results reveal that the Bayes estimator using gamma priors via the MCMC method outperforms other approaches for small values of \(\eta \) . For moderate values of \(\eta \) , the Bayes estimator based on Lindley’s approximation demonstrates superior accuracy. In contrast, for large values of \(\eta \) , classical methods’particularly the maximum likelihood estimator’exhibit the best performance in terms of the lowest mean squared error. Furthermore, the Bayesian credible intervals with gamma priors consistently attain the narrowest average widths while maintaining the desired coverage probabilities. A real data analysis is also carried out to demonstrate the practical applicability of the proposed methods.
