The emergence of advanced technologies has driven businesses to develop more complex and durable products, thereby increasing competition in global markets. As a result, conducting reliability tests has become crucial for assessing a product reliability. This paper aims to estimate the stress–strength reliability parameter \(\Omega = P(Y < X)\) , where the strength variable (X ) and stress variable (Y ) are independent Lomax random variables. In practical situations, the stress variable represents operational circumstances, external disruptions, or operators’ behavior, which can reduce the strength variable and compromise system reliability. Based on this reliability analysis, a partially accelerated life test is employed to reduce testing duration by subjecting the system to more severe conditions than usual. To generate data, a progressive Type II censoring scheme is used to strike a balance between the duration of the test, the desired sample size, and the associated costs. The estimation of model parameters and \(\Omega \) was conducted using the maximum likelihood approach. Additionally, several interval estimation techniques were employed, including the asymptotic confidence intervals, percentile bootstrap, bias-corrected bootstrap, bias-corrected and accelerated bootstrap, and bootstrap Student’s t confidence intervals. Bayesian estimates, along with their highest posterior density credible intervals, are computed using the Markov Chain Monte Carlo approach, specifically employing the Gibbs sampler algorithm. A simulation study is performed to examine the proposed estimation techniques and compare their performance across different sample sizes. Furthermore, the approaches are applied to real industrial data to validate the theoretical analysis.
