Stochastic comparison of lifetimes of two (n−k+1)-out-of-n systems with heterogeneous dependent components

Mohsen Rezapour and Mohammad Hossein Alamatsaz

Journal of Multivariate Analysis, 2014, vol. 130, issue C, 240-251

Abstract: 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.

Keywords: Dependent sample; Order statistics; Stochastic ordering; Reliability; Copula (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:130:y:2014:i:c:p:240-251

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DOI: 10.1016/j.jmva.2014.05.009

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