The strength-stress reliability (SSR) system, denoted as \(R=P(X > Y)\) , is widely employed to assess the probability that a system’s strength exceeds its applied stress, making it essential in various scientific and engineering fields. Efficient estimation of this system is essential. The except extreme ranked set sampling (EERSS) method provides an effective alternative for parameter estimation by reducing the required sample size without compromising precision. This study proposes new estimators of SSR using the novel EERSS approach, assuming that both strength and stress follow an exponential distribution. We utilize maximum likelihood (ML) and modified maximum likelihood (MML) estimation techniques to estimate \(R\) . Additionally, we derive the asymptotic distribution, asymptotic confidence interval (ACI), and asymptotic relative efficiency (ARE). The performance of the new estimators is compared with their counterparts under simple random sampling (SRS) and ranked set sampling (RSS). The ARE and ACI results indicate that the newly introduced ML estimator outperforms both SRS and RSS estimators. A simulation study was performed to evaluate the performance of the new estimator. The results show that the ML and MML estimators based on EERSS consistently outperform their SRS and RSS counterparts in terms of relative efficiency and lower mean square error. Furthermore, two real-world applications confirm these findings, illustrating the practical utility of EERSS in reliability estimation.
