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On the Importance of Copula Choice in the Reliability Evaluation of Dependent Stress-Strength Models | ||
| Journal of Mathematics and Modeling in Finance | ||
| دوره 5، شماره 2، دی 2025، صفحه 217-252 اصل مقاله (339.83 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2025.86896.1196 | ||
| نویسنده | ||
| Nooshin Hakamipour* | ||
| Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. | ||
| چکیده | ||
| Reliability assessment, vital in high-stakes engineering, often employs the stress-strength model. However, traditional models frequently assume independence between stress and strength, an assumption that can lead to inaccurate reliability estimates when dependence exists due to real-world factors. To address this, the current study proposes a dependent stress-strength model using copula theory, which flexibly models dependence by separating marginal and joint distributions. Four copula families—Farlie-Gumbel-Morgenstern, Ali-Mikhail-Haq, Gumbel's bivariate exponential, and Gumbel-Hougaard—are investigated for their ability to capture diverse dependency patterns. The Inverse Lomax distribution is utilized for both stress and strength marginals due to its suitability for heavy-tailed reliability data. The copula dependence parameter θ is estimated via conditional likelihood and Blomqvist's beta-based method of moments. The asymptotic distributions of these estimators are derived, and their performance is evaluated through extensive simulations. The research thoroughly examines how system reliability R changes with $\theta$ across various model configurations. Findings indicate that the Gumbel-Hougaard copula demonstrates the highest sensitivity of $R$ to θ, effectively capturing a wide range of dependency strengths. This paper highlights the critical need to incorporate dependence in stress-strength models and offers practical guidance for copula selection, thereby enhancing the accuracy and robustness of reliability predictions in complex engineering systems. A practical examination of a real dataset is conducted to demonstrate the concept. | ||
| کلیدواژهها | ||
| Ali-Mikhail-Haq؛ Blomqvist’s beta؛ Copula؛ Farlie-Gumbel-Morgenstern؛ Gumbel-Hougaard؛ Reliability | ||
| مراجع | ||
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