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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 | ||
| دوره 4، شماره 1، مهر 2024، صفحه 1-17 اصل مقاله (194.66 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22054/jmmf.2024.78338.1124 | ||
| نویسنده | ||
| Nooshin Hakamipour* | ||
| Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran. | ||
| چکیده | ||
| The stress-strength model is a commonly utilized topic in reliability studies. In many reliability analyses involving stress-strength models, it is typically assumed that the stress and strength variables are unrelated. Nevertheless, this assumption is often impractical in real-world scenarios. This research assumes that the strength and stress variables follow the Pareto distribution, and a Gumbel copula is employed to represent their relationship. Additionally, the data is gathered through the Type-I progressively hybrid censoring scheme. The method of maximum likelihood estimation is used for point estimation, while asymptotic and Bootstrap percentile confidence intervals are employed for interval estimation of the unknown parameters and system reliability. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, an actual dataset is examined to showcase the practicality of the stress-strength model. Simulation is employed to assess the effectiveness of the suggested estimators. Subsequently, a real dataset is examined to demonstrate the practicality of the stress-strength model. | ||
| کلیدواژهها | ||
| Bootstrap percentile confidence interval؛ Gumbel copula؛ Pareto distribution؛ Multicomponent dependent stress-strength model؛ Type-I progressively hybrid censoring scheme | ||
| مراجع | ||
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[1] E. K. Al-Hussaini and M. Hussein, Estimation using censored data from exponentiated Burr type XII population, American Open Journal of Statistics, 1 (2011), 33-45. [2] D. K. Al-Mutairi, M. E. Ghitany, and D.Kundu, Inferences on stress-strength reliability from Lindley distributions, Communications in Statistics-Theory and Methods, 42(8) (2013), 1443-1463. [3] A. Asgharzadeh, M. Kazemi, and D. Kundu, Estimation of P(X > Y ) for Weibull distribution based on hybrid censored samples, International Journal of System Assurance Engineering and Management, 8(1) (2015), 489-498. [4] X. Bai, Y. Shi, Y. Liu, and B. Liu, Reliability estimation of multicomponent stress-strength model based on copula function under progressively hybrid censoring, Journal of Computational and Applied Mathematics, 344 (2018), 100-114. [5] Z. W. Birnbaum, On a use of the MannWhitney statistic, In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, (1 (1956), 13-17), Berkeley, CA, USA: University of California Press. [6] S. Dey and F. A. Moala, Estimation of reliability of multicomponent stress-strength of a bathtub shape or increasing failure rate function, International Journal of Quality and Reliability Management, 36(2) (2019), 122-136. [7] S. Dey, J. Mazucheli and M. Z. Anis, Estimation of reliability of multicomponent stressstrength for a Kumaraswamy distribution, Communications in Statistics-Theory and Methods, 46(4) (2017) 1560-1572. [8] F. Domma, and S. Giordano, A stressstrength model with dependent variables to measure household financial fragility, Statistical Methods and Applications, 21(3) (2012), 375-389. [9] B. Efron, The jackknife, the bootstrap and other resampling plans, Society for industrial and applied mathematics (1982). [10] N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distribution, Vol. 1, John Wiley & Sons, New York, 1994. [11] T. Kayal, Y. M. Tripathi, S. Dey, and S. J. Wu, On estimating the reliability in a multicomponent stress-strength model based on Chen distribution, Communications in StatisticsTheory and Methods, 49(10) (2020), 2429-2447. [12] F. Kzlaslan and M. Nadar, Estimation of reliability in a multicomponent stressstrength model based on a bivariate Kumaraswamy distribution, Statistical Papers, 59(1) (2016), 1-34. [13] D. Kundu, and M. Z. Raqab, Estimation of R = P[Y < X] for three-parameter generalized Rayleigh distribution, Journal of Statistical Computation and Simulation, 85(4) (2015), 725- 739. [14] B. Liu, Y. Shi, H. K. T. Ng and X. Shang, Nonparametric Bayesian reliability analysis of masked data with dependent competing risks, Reliability Engineering & System Safety, 210 (2021), 107502. [15] A. M. Mansour, A. E. R. Nada, and A. H. Mehana, Effect of noise variance estimation on channel quality indicator in LTE systems, In 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP) (2015, December) (pp. 156-160). IEEE. [16] C. A. McGilchrist and C. W. Aisbett, Regression with frailty in survival analysis, Biometrics, 47(2) (1991), 461-466. [17] M. Nadar and F. Kzlaslan, Estimation of reliability in a multicomponent stressstrength model based on a MarshallOlkin bivariate Weibull distribution, IEEE Transactions on Information Theory, 65(1) (2015), 370-380. [18] S. Nadarajah, Reliability for some bivariate gamma distributions, Mathematical Problems in Engineering, 2005(2), (2005) 151-163. [19] P. Nasiri, Estimation of R = P(Y < X) for two-parameter exponential distribution, Australian Journal of Basic and Applied Sciences, 5(12) (2011), 414-20. [20] J. Navarro and F. Durante, opula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components, Journal of Multivariate Analysis, 158 (2017), 87-102. [21] B. Nelsen, An Introduction to Copulas, second ed. Springer Science & Business Media, (2006), New York. [22] G. S. Rao, Estimation of reliability in multicomponent stressstrength based on generalized exponential distribution, Journal of Statistical Theory and Applications, 9(1) (2013), 1935. [23] G. S. Rao, M. Aslam and O. H. Arif, Estimation of reliability in multicomponent stressstrength based on two parameter exponentiated Weibull distribution, Communications in Statistics-Theory and Methods, 46(15) (2016), 74957502. [24] G. S. Rao, M. Aslam and D. Kundu, Burr-XII distribution parametric estimation and estimation of reliability of multicomponent stressstrength, Communications in Statistics-Theory and Methods, 44(23) (2015), 49534961. [25] A. Sklar, Functions de repartition a n dimensions et leurs marges, In Annales de l’ISUP 8(3) (1959), pp. 229231. [26] Y. H. Wei and S. Y. Zhang, Copulas theory and its application in financial analysis, Beijing, Tsinghua University Press (2008). [27] A. Wong, Interval estimation of P(Y < X) for generalized Pareto distribution, Journal of Statistical Planning and Inference, 142(2) (2012), 601607. | ||
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