Stochastic comparison of lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent components.
In: Journal of Multivariate Analysis, Jg. 130 (2014-09-01), S. 240-251
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In this paper, we shall generalize stochastic comparison of lifetimes of two (n-k+1)-out-of-n systems of possibly dependent lifetimes. The type of dependency assumed throughout this paper is according to Archimedean copulas with n-monotone and completely monotone (cm) generators. In fact, we provide certain conditions under which one can compare lifetimes of two (n-k+1)-out-of-n systems with dependent components with respect to usual stochastic ordering. We also consider the Archimedean copula with an n-monotone generator obtained by gamma distribution (which generates Gamma-Simplex Copulas described in McNeil and Nešlehovà (2010) [19]). The cumulative distribution function (cdf) of the lifetime of an (n-k+1)-out-of-n system with dependent components is also obtained. Then, some trivial conditions under which one can compare lifetimes of two (n-k+1)-out-of-n systems in this case are provided. The cdf of order statistics arising from a random vector whose dependence structure is described by an Archimedean copula with a cm generator is also obtained. Some simple conditions under which one can compare lifetimes of two (n-k+1)-out-of-n systems in this case are investigated. Finally, we shall generalize the results of Ma (1997), which compare lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent populations and homogeneous dependent populations, for samples with dependent components. [ABSTRACT FROM AUTHOR]
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Stochastic comparison of lifetimes of two (n-k+1)-out-of-n systems with heterogeneous dependent components.
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Autor/in / Beteiligte Person: | Rezapour, Mohsen ; Alamatsaz, Mohammad Hossein |
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Zeitschrift: | Journal of Multivariate Analysis, Jg. 130 (2014-09-01), S. 240-251 |
Veröffentlichung: | 2014 |
Medientyp: | academicJournal |
ISSN: | 0047-259X (print) |
DOI: | 10.1016/j.jmva.2014.05.009 |
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