Analysis of Stress-Strength Modeling utilizing Median-Ranked Set Sampling with its Illustration

This study focuses on the estimation of stress–strength reliability models, specifically Formula: see text in the first model, where both the strength variable Formula: see text and stress variable Formula: see text follow the identical distribution, and Formula: see text in the second model, where the strength variable Formula: see text and stress variable Formula: see text have distinct distributions. In the first model, we assume that the stress variable Formula: see text and the strength variable Formula: see text follow generalized exponential distributions. In contrast, in the second model, the strength variable Formula: see text is assumed to have a generalized exponential distribution, while the stress variable Formula: see text follows the Weibull distribution. The research utilizes the median-ranked set sampling (MRSS) technique to investigate different scenarios, operating on the premise that the variables in models are independent. The research utilizes the MRSS technique to investigate different scenarios, operating on the premise that the variables in both models are independent. By employing the maximum likelihood technique and implementing an MRSS design, we derive the reliability estimators for both models, considering situations where the strength and stress variables may have similar or dissimilar set sizes. A simulation study is conducted to validate the precision and accuracy of different estimations. In the majority of cases, the simulation results demonstrate that the reliability estimates for the first model are more precise than those for the second model. Also, the first model’s reliability is always more than the reliability estimate of the second model. Survival data are utilized to illustrate the concepts, enabling the verification of the theoretical findings.