Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 2025 07 08 On the dependency in stress-strength models 9817 10.22075/ijnaa.2024.34563.5166 EN Saeed Zalzadeh Department of Statistics, Semnan University, Semnan, Iran 0000-0002-3417-5453 Journal Article 2024 05 25 In reliability studies, the probability $R = P(Y < X)$ is called “reliability”,  and  $X, Y$  are typically considered independent. However, in many applications, such an assumption may be unrealistic. In this paper, we consider the stress-strength reliability $R = P(Y < X)$ where the stress $Y$ and strength $X$ are dependent. We use a copula to describe dependence among random variables $X$ and $Y$. We obtain $R$ for several copula functions with exponential marginal and plot graphs of $R$ versus the dependence parameter to study the effect of (positive and negative) dependency on $R$. https://ijnaa.semnan.ac.ir/article_9817_73740ea85c4ec25f00f9acbd859f861d.pdf