This study addresses the challenge of efficiently estimating the lifetime of highly reliable products by developing inference for the stress-strength reliability parameter \( R = P(X > Y) \) , where the strength variable \( X \) is subjected to a random stress variable \( Y \) . Both variables are assumed to follow the Lomax distribution. To shorten the reliability assessment process, a partially accelerated life test is implemented in conjunction with a Type-II hybrid censoring scheme. Two advanced Bayesian approaches, namely E-Bayesian estimation and hierarchical Bayesian estimation, are employed to estimate the stress-strength parameter \( R \) . Moreover, highest posterior density credible intervals are obtained through a Markov Chain Monte Carlo framework using the Gibbs sampler and Metropolis–Hastings algorithms. Simulation studies under various sample sizes and censoring scenarios are conducted to evaluate the performance of the proposed estimators. Finally, the methodologies are applied to real industrial data to demonstrate their practical usefulness and to validate the theoretical findings.
