On the Mean Residual Lifetime at System Level in Two-Component Parallel Systems for the FGM Distribution FULL TEXT

Year 2012, Volume: 41 Issue: 1, 139 - 145, 01.01.2012

Burcu Ucer Selma Gurler

Keywords

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References

• 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.
• 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.
• Bairamov, I. G. and Kotz, S. Dependence structure and symmetry of Huang-Kotz FGM distributions and their extensions, Metrika 56, 55–72, 2002.
• Bairamov, I. G. and Parsi, S. Order statistics from mixed exchangeable random variables, Journal of Computational and Applied Mathematics 235 (16), 4629–4638, 2011.
• David, H. A. and Nagaraja, H. N. Order Statistics (Wiley Series in Probability and Statistics, New Jersey, 2003).
• Farlie, D. J. G. The performance of some correlation coeffcients for a general bivariate dis- tribution, Biometrika 47, 307–323, 1960.
• Gumbel, E. J. Bivariate exponential distributions, Journ. Amer. Statist. Assoc. 55, 698–707, 1960. [8] Gurler, S. On residual lifetimes in sequential (n −k +1)-out-of-n systems, Statistical Papers 53, 23–31, 2012.
• Huang, J. S. and Kotz, S. Correlation structure in iterated Farlie-Gumbel-Morgenstern dis- tributions, Biometrika 71, 633–636, 1984.
• Johnson, N. L. and Kotz, S. On some generalized Farlie-Gumbel-Morgenstern distributions, Communications in Statistics-Theory and Methods 4, 415–427, 1975.
• Li, X. and Zhang, Z. Some stochastic comparisons of conditional coherent systems, Applied Stochastic Models in Business and Industry 24, 541–549, 2008.
• Morgenstern, D. Einfache Beispiele zweidimensionaler Verteilungen, Mitteilungsblatt fur Mathematishe Statistik 8, 234–235, 1956.
• Navarro, J. and Hernandez, P. J. Mean residual life functions of finite mixtures, order sta- tistics and coherent systems, Metrika 67 (3), 277–298, 2008.
• 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.
• Navarro, J., Ruiz, J. M. and Sandoval, C. J. Reliability properties of systems with exchange- able components and exponential distributions, Test 15 (2), 471–484, 2006.
• Navarro, J. and Rychlik, T. Reliability and expectation bounds for coherent systems with exchangeable components, Journal of Multivariate Analysis 98, 102–113, 2007.
• Navarro, J. and Spizzichino, F. Comparisons of series and parallel systems with components sharing the same copula, Applied Stochastic Models in Business and Industry 26, 775–791, 2010. [18] Navarro, J., Spizzichino, F. and Balakrishnan, N. Applications of average and projected systems to the study of coherent systems, J. Multivariate Analysis 101, 1471–1482, 2010.
• Nelsen, R. B. An Introduction to Copulas (Springer Verlag, New York, 1999).
• Poursaeed, M. H. A Note on the mean past and the mean residual life of a (n-k+1)-out-of-n system under multi monitoring, Statistical Papers 51 (2), 409–419, 2010.
• Sadegh, M. K. Mean past and mean residual life functions of a parallel system with non- identical components, Communications in Statistics-Theory and Methods 37 (7), 1334–1145, 2008. [22] Zhao, P. and Balakrishnan, N. MRL ordering of parallel systems with two heterogeneous components, Journal of Statistical Planning and Inference 141, 631–638, 2011.