Evaluating Stress-Strength Reliability Estimation Technique: A Study on Ranked Set Sampling for the Beta-Lomax Distribution

Reliability, a crucial aspect in engineering and project management, signifies the likelihood of a system or project enduring without malfunction over a specified duration. Typically, the random variable X embodies the lifespan of the system or project. Stress-strength reliability, on the other hand, gauges the assurance that a product or process remains unaffected by stress Y. Extensive literature explores the point estimation and testing of R(t) = P(X > t) (the survival function of the random variable), and P = P(Y < X), delving into methods to enhance reliability assessment. This paper delves into the estimation of R(t) and stress-strength reliability P through ranked set sampling (RSS), assuming independence between stress Y and strength X, both following the Beta-Lomax (BL) distribution. Through rigorous analysis, the maximum likelihood (ML) estimator for R(t) and P is derived, subsequently juxtaposed with its simple random sampling (SRS) equivalent to gauge performance. By applying this methodology to real data from Wheaton River, the study underscores the practicality and efficacy of the proposed approach. By offering a comprehensive analysis of reliability and stress-strength reliability estimation utilizing RSS and the BL distribution, this research furnishes valuable insights for practitioners and researchers in the field. The integration of innovative sampling techniques and statistical methodologies not only enhances the precision of estimations but also underscores the importance of robust reliability assessments in ensuring the longevity and efficiency of systems and projects.