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Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 1

On the mean residual lifetime at system level in two-component parallel systems for the FGM distribution

Selma GURLER
Burcu UCER
Pages
139–145
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Applications of these results to evaluate the relationship between the mean residual life and that of the dependence of components are also given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider the mean residual lifetime of two-component parallel systems in the case of possibly dependent components.
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Key Findings & Data:We provide some results and examine the behavior of the mean residual life function at the system level for the bivariate Farlie-Gumbel- Morgenstern (FGM) distribution.
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Conclusion & Impact:Applications of these results to evaluate the relationship between the mean residual life and that of the dependence of components are also given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we consider the mean residual lifetime of two-component parallel systems in the case of possibly dependent components. We provide some results and examine the behavior of the mean residual life function at the system level for the bivariate Farlie-Gumbel- Morgenstern (FGM) distribution. Applications of these results to evaluate the relationship between the mean residual life and that of the dependence of components are also given.

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Cite This Article

GURLER, S., UCER, B. (2022). On the mean residual lifetime at system level in two-component parallel systems for the FGM distribution. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 1, 139–145. https://ajindex.com/articles/530525

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References (17)

  1. Asadi, M. and Bairamov, I. G. A note on the mean residual life function of a parallel system, Communications in Statistics-Theory and Methods 34(2), 475-484, 2005
  2. Bairamov, I.G., Ahsanullah, M. and Akhundov, I. A residual life function of a system having parallel or series structure, J. Statist. Theor. Appl. 1 (2), 119-132, 2002
  3. Bairamov, I. G. and Kotz, S. Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions, Metrika 56, 55-72, 2002
  4. Bairamov, I. G. and Parsi, S. Order statistics from mixed exchangeable random variables, Journal of Computational and Applied Mathematics 235(16), 4629-4638, 2011
  5. David, H. A. and Nagaraja, H. N. Order Statistics (Wiley Series in Probability and Statistics, New Jersey, 2003)
  6. Far lie, D. J. G. The performance of some correlation coeff'cients for a general bivariate distribution, Biometrika 47, 307-323, 1960
  7. Gumbel, E.J. Bivariate exponential distributions, Journ. Amer. Statist. Assoc. 55, 698-707, 1960
  8. Gürler, S. On residual lifetimes in sequential (n — k + l)-out-of-n systems, Statistical Papers 53, 23-31, 2012
  9. Huang, J.S. and Kotz, S. Correlation structure in iterated Farlie-Gumbel-M org enstern distributions, Biometrika 71, 633-636, 1984
  10. Johnson, N. L. and Kotz, S. On some generalized Farlie-Gumbel-M org enstern distributions, Communications in Statistics-Theory and Methods 4, 415-427, 1975
  11. Li, X. and Zhang, Z. Some stochastic comparisons of conditional coherent systems, Applied Stochastic Models in Business and Industry 24, 541-549, 2008
  12. Morgenstern, D. Einfache Beispiele zweidimensionaler Verteilungen, Mitteilungsblatt fur Mathematishe Statistik 8, 234-235, 1956
  13. Navarro, J. and Hernandez, P.J. Mean residual life functions of finite mixtures, order statistics and coherent systems, Metrika 67(3), 277-298, 2008
  14. Navarro, J. and Lai, C. D. Ordering properties of systems with two dependent componens, Communications in Statistics-Theory and Methods 36(3), 645-655, 2007
  15. Navarro, J., Ruiz, J.M. and Sandoval, C.J. Reliability properties of systems with exchangeable components and exponential distributions, Test 15(2), 471-484, 2006
  16. Navarro, J. and Rychlik, T. Reliability and expectation bounds for coherent systems with exchangeable components, Journal of Multivariate Analysis 98, 102-113, 2007
  17. Navarro, J. and Spizzichino, F. Comparisons of series and parallel systems with components sharing the same copula, A