In this article, we consider the situation in estimating the reliability: \(\Re = P(X<Y<Z)\) . Here, the strength level Y should exceed the lower-bound stress level X and be below the upper-bound stress level Z. The estimate of \(\Re \) is considered using frequentist and Bayesian techniques when stress random variables (X, Z) and the strength random variable (Y) follow a unit exponentiated half-logistic distribution. We address this issue when the stress and strength data regarding upper-record ranked set samples are expressed. Point and confidence interval estimates of \(\Re \) are obtained using the maximum likelihood and parametric bootstrapping approaches. This study considers the stress-strength reliability estimator with uniform and gamma priors under several loss functions. The estimate of \(\Re \) is generated using Metropolis-Hastings samplers and Bayesian analyses based on the suggested loss functions. Additionally, credible intervals with the highest posterior densities are constructed. Monte Carlo simulations are performed to analyze the behavior of the proposed estimators. Two numerical examples are provided to illustrate the results: the breaking strengths of jute fibers at three different gauge lengths and the amount of rainfall (in inches) recorded at the Los Angeles Civic Center. In conclusion, the results indicate that the mean squared error values decrease with increasing sample size. In most cases, Bayesian estimates under the precautionary loss function perform better in terms of simulation results than other specified loss functions. The average length and coverage probability for the confidence interval based on the parametric percentile bootstrap methods are consistent with those based on the parametric bootstrap-t method.
