Estimating Stress-Strength Reliability in the Beta-Pareto Distribution Using Ranked Set Sampling

This paper introduces a novel approach for estimating the stress-strength reliability in the beta-pareto ($BP$) distribution by employing ranked set sampling ($RSS$). Stress-strength reliability is a crucial measure that quantifies the probability of an item or system operating without failure under random stress and strength conditions. The study focuses on estimating the reliability function ($R(t)$) and the probability ($P$) of stress being lower than strength when both stress and strength variables follow independent random variables from the $BP$ distribution. The maximum likelihood $ML$ estimator of $R(t)$ and $P$ is obtained, and its performance is compared with the estimator based on simple random sampling ($SRS$). The proposed methodology is evaluated using real data from the Wheaton River experiment, showcasing its practical applicability and effectiveness. The findings highlight the superiority of our approach in accurately estimating stress-strength reliability in the $BP$ distribution, providing valuable insights for various fields such as engineering, finance, and risk analysis.