This research focuses on estimating the stress-strength reliability in a system characterized by the influence of two random stresses on its strength, employing both frequentist and Bayesian approaches. The reliability of such systems is represented by the function \(\delta =\textrm{P}(U<V<W)\) , where V denotes the system’s strength, and U and W represent the stresses. The analysis is performed under a progressive Type-II censoring scheme, considering the random variables U, V, and W as independent and following the Burr-XII distribution. In a frequentist setup, both the maximum likelihood estimator and the maximum product spacings estimator of \(\delta\) have been obtained. In the Bayesian paradigm, the Bayes estimator of \(\delta\) under the squared error loss function is derived utilizing the Markov chain Monte Carlo method, considering independent gamma priors for the unknown parameters. In addition, asymptotic confidence intervals and highest probability density credible intervals for \(\delta\) are also formulated. An extensive simulation experiment is carried out to compare the performances of the different developed estimators. Finally, a real-life application is presented to demonstrate the practical applicability of the proposed theory.
