Article ID Journal Published Year Pages File Type
1145737 Journal of Multivariate Analysis 2014 12 Pages PDF
Abstract

In this paper, we shall generalize stochastic comparison of lifetimes of two (n−k+1)(n−k+1)-out-of-nn systems of possibly dependent lifetimes. The type of dependency assumed throughout this paper is according to Archimedean copulas with nn-monotone and completely monotone (cm) generators. In fact, we provide certain conditions under which one can compare lifetimes of two (n−k+1)(n−k+1)-out-of-nn systems with dependent components with respect to usual stochastic ordering. We also consider the Archimedean copula with an nn-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)(n−k+1)-out-of-nn system with dependent components is also obtained. Then, some trivial conditions under which one can compare lifetimes of two (n−k+1)(n−k+1)-out-of-nn 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)(n−k+1)-out-of-nn systems in this case are investigated. Finally, we shall generalize the results of Ma (1997), which compare lifetimes of two (n−k+1)(n−k+1)-out-of-nn systems with heterogeneous dependent populations and homogeneous dependent populations, for samples with dependent components.

Related Topics
Physical Sciences and Engineering Mathematics Numerical Analysis
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