| تعداد نشریات | 63 |
| تعداد شمارهها | 2,268 |
| تعداد مقالات | 18,694 |
| تعداد مشاهده مقاله | 58,231,266 |
| تعداد دریافت فایل اصل مقاله | 29,905,623 |
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 | ||
|
[1] N. Blomqvist, On a measure of dependence between two random variables, The Annals of Mathematical Statistics, 21:593–600, 1950. [2] I. M. Chakravarti, R. G. Laha, and J. Roy, Handbook of methods of applied statistics, New York: Wiley, 1967. [3] J. D. Church, B. Harris, The Estimation of Reliability from Stress–Strength Relationships, Technometrics, 12:49–54, 1970. [4] F., Domma, S. Giordano, A copula-based approach to account for dependence in stress– strength models, Statistical Papers, 54:807–826, 2013. [5] M. Emile, J. Gumbel ´ , Distributions des valeurs extremes en plusieurs dimensions, In Annales de l’ISUP, 9:171–173, 1960. [6] R. C. Gupta, M. E. Ghitany, and D. K. Al-Mutairi, Estimation of Reliability from a Bivariate Log-Normal Data, Journal of Statistical Computation and Simulation, 83:1068– 1081, 2012. [7] C. Genest, A. Carabar´ın-Aguirre, and F. Harvey, Copula parameter estimation using Blomqvist’s beta, Journal de la Soci´et´e Fran¸caise de Statistique, 154:5–24, 2013. [8] N. Hakamipour, Gumbel copula-based reliability assessment to describe the dependence of the multicomponent stress–strength model for Pareto distribution, Journal of Mathematics and Modeling in Finance, 4:1–17, 2024. [9] N. Hakamipour, Stress–strength reliability estimation of s-out-of-k multicomponent systems based on copula function for dependent strength elements under progressively censored sample, International Journal of General Systems, 2024, https://doi.org/10.1080/03081079.2024.2405687. [10] N. Hakamipour, Copula for Dependent Competing Risks Model in ProgressiveStress Accelerated Life Tests, Quality and Reliability Engineering International, 2025, https://doi.org/10.1002/qre.3811. [11] P. Hougaard, A class of multivanate failure time distributions, Biometrika, 73:671–678, 1986. [12] J. Hu, Y. Zhuang, and C. Goldiner, Fixed-Accuracy Confidence Interval Estimation of P(X < Y ) under a Geometric–Exponential Model, Japanese Journal of Statistics and Data Science, 4:1079–1104, 2021. [13] Y. F. Jamilu, A. U. Adamu, Y. Aliyu, and I. I. Aliyu, The Inverse Lomax distribution with applications, In Royal Statistical Society Nigeria Local Group Annual Conference Proceedings, pages 105–112, 2025.. [14] H. Joe, Multivariate Models and Dependence Concepts Monographs on Statistics and Applied Probability, Chapmann & Hall London, 1997. [15] M. Jovanovic, V. Raji ´ c´, Estimation of P(X < Y ) for Geometric-Exponential Model Based on Complete and Censored Samples, Communications in Statistics – Simulation and Computation , 46:3050–3066, 2017. [16] M. Jovanovic, V. Raji ´ c´, Estimation of P(X < Y ) for gamma exponential model, CYUJOR , 24:283–291, 2014. [17] S. Nadarajah, Reliability for Some Bivariate Beta Distributions, Mathematical Problems in Engineering, 2:101–111, 2005. [18] R. B. Nelsen, An Introduction to Copulas, Springer, New York, 1999. [19] D. Patil, U. V. Naik-Nimbalkar, and M. M. Kale, Effect of Dependency on the Estimation of P[Y < X] in Exponential Stress–strength Models, Austrian Journal of Statistics, 51:10–34, 2022. [20] D. Patil, U. V. Naik-Nimbalkar, and M. M. Kale, Estimation of P[Y < X] for dependence of stress–strength models with Weibull marginals, Annals of Data Science 11:1303–1340, 2024. [21] F. Schmid, R. Schmidt, Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence, Metrika, 66:323–354, 2007. [22] S. Sengupta, Unbiased Estimation of P(X > Y ) for Two-Parameter Exponential Populations Using Order Statistics, Statistics, 45:179–188, 2011. [23] A. Sharma, P. Kumar, Estimation of Density and Reliability Function of Inverse Lomax Distribution under Type-II Censoring and the Sampling Scheme of Bartholomew, International Journal of Applied Mathematics and Statistics, 59:129–150, 2020. [24] S. K. Singh, U. Singh, and D. Kumar, Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors, Journal of Statistical computation and simulation, 83:2258–2269, 2013. [25] A. Sklar, Fonctions De Repartition´e n Dimensions Et Leurs Marges, Publications de l’Institut de Statistique de l’Universit´e de Paris, 8:229–231, 1959.. [26] A. H. Tolba, D. A. Ramadan, E. M. Almetwally, T. M. Jawa, and N. Sayed-Ahmed, Statistical inference for stress–strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications, Thermal Science, 26(Spec. issue 1):303–326, 2022. [27] A. Wong, Interval Estimation of P(Y < X) for Generalized Pareto Distribution, Journal of Statistical Planning and Inference, 142:601–607, 2012. [28] T. Xavier, J. K. Jose, Stress–strength reliability estimation involving paired observation with ties using bivariate exponentiated half-logistic model, Journal of Applied Statistics, 49:1049–1064, 2012. | ||
|
آمار تعداد مشاهده مقاله: 2,625 تعداد دریافت فایل اصل مقاله: 197 |
||