Stress-strength models are widely used to assess the reliability of systems under uncertain conditions. While most studies assume independence between stress and strength variables, such an assumption may be unrealistic in many practical situations where these components are inherently dependent. In this study, we investigate stress-strength reliability under a dependent framework, where both stress and strength variables follow modified Weibull distributions and their dependence is modeled via a Clayton copula. The proposed model allows distinct parameter sets, resulting in a flexible seven-parameter structure that extends Weibull-based models. We consider several estimation procedures for the model parameters and reliability, including two-step maximum likelihood, least squares, weighted least squares, and maximum product of spacings, with interval estimation obtained via asymptotic and bootstrap confidence intervals. The performance of the proposed estimators is evaluated through an extensive Monte Carlo simulation study under various parameter configurations and sample sizes. Finally, the applicability of the proposed model is illustrated using monthly occupancy data from Istanbul's two largest dams, with the Clayton copula capturing their dependence structure. This application demonstrates how stress-strength reliability can inform water management decisions and mitigate inter-regional operational risks.

翻译：应力-强度模型被广泛应用于评估系统在不确定条件下的可靠性。尽管大多数研究假设应力与强度变量相互独立，但在许多实际场景中，这些变量存在内在依赖关系，此类假设可能并不现实。本研究在相依框架下探讨应力-强度可靠性，其中应力与强度变量均服从修正威布尔分布，其相依性通过Clayton copula建模。所提模型允许不同的参数集，形成灵活的结构（共七个参数），扩展了基于威布尔的模型。我们考虑了多种参数及可靠性估计方法，包括两步极大似然估计、最小二乘估计、加权最小二乘估计及最大间距积估计，并通过渐近置信区间和自助法置信区间进行区间估计。通过在不同参数配置及样本量下开展广泛的蒙特卡洛模拟研究，评估了所提估计量的性能。最后，利用伊斯坦布尔两大水库的月蓄水量数据展示了所提模型的适用性，其中Clayton copula捕捉了其依赖结构。该应用示例阐明了应力-强度可靠性如何为水资源管理决策提供依据，并降低跨区域运营风险。