Real-world constraints like time and sample size limitations often restrict access to complete data. Consequently, it is beneficial to study estimation problems based on information from existing data. In these circumstances, employing a suitable sampling strategy to obtain more effective estimators is crucial. In this study, we addressed the estimation of the stress-strength reliability parameter $\zeta$ based on lower record ranked set sampling. The stress and strength variables adhere to the exponentiated Pareto distribution with a common second shape parameter. The maximum likelihood and Bayesian estimation methods are suggested for estimating $\zeta .$ The Bayesian estimator is provided in the case of gamma and uniform priors using different loss functions. Two distinct parametric bootstrap techniques are established, and Bayesian credible intervals are generated with the help of the Markov chain Monte Carlo method. A comprehensive Monte Carlo simulation study was developed to evaluate the precision of different estimators. A simulation study highlighted that the Bayesian estimates, which are calculated under different loss functions, perform more effectively than a comparable maximum likelihood estimates. It was discovered that the percentile bootstrap method produced better estimates than the normal-bootstrap method, with shorter average lengths and higher coverage probability. Two datasets from physical scientific applications further support the effectiveness and usefulness of the methodology.