Reliability analysis under extreme conditions for the Burr XII distribution utilizing upper record values

This article examines the reliability estimation scenario of $\omega = P(L\lt Y\lt T),$ where the strength $Y$ occurs between two extreme conditions, namely the upper extreme ($T$) and the lower extreme ($L$). Assuming that the random variables $L, T,$ and $Y$ follow a Burr XII distribution, the statistical inference of $\omega$ is examined under the upper values of the record. Maximum likelihood and parametric bootstrapping approaches are used to obtain point and confidence interval estimates of $\omega$. This study considers the stress-strength reliability estimator with uniform and gamma priors under several loss functions. Based on the proposed loss functions, reliability $\omega$ is estimated using Bayesian analyzes with Gibbs and Metropolis-Hastings samplers. In addition, we construct credible intervals that contain the highest posterior densities. Monte Carlo simulation studies and examples based on real-data are also performed to analyze the behavior of the proposed estimators. This study involves the examination of specimens of an electrically insulating fluid, especially those utilized in transformers, by applying the stress-strength model for data set analysis. Based on the study's results, it was clear that mean squared errors decreased as record numbers increased. Bayesian estimates under the precautionary loss function are commonly found to be more suitable for determining simulation conclusions than other specified loss functions.