Ordering and aging properties of systems with dependent components governed by the Archimedean copula

Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that...

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Bibliographic Details
Published inProbability in the engineering and informational sciences Vol. 37; no. 1; pp. 1 - 28
Main Authors Sahoo, Tanmay, Hazra, Nil Kamal
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.01.2023
Subjects
Aging
Lifetime
Random variables
Coherent system
60E15
Stochastic orders
Archimedean copula
90B25
r-out-of-n system
Stochastic agings
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Summary:Copula is one of the widely used techniques to describe the dependency structure between components of a system. Among all existing copulas, the family of Archimedean copulas is the popular one due to its wide range of capturing the dependency structures. In this paper, we consider the systems that are formed by dependent and identically distributed components, where the dependency structures are described by Archimedean copulas. We study some stochastic comparisons results for series, parallel, and general $r$-out-of-$n$ systems. Furthermore, we investigate whether a system of used components performs better than a used system with respect to different stochastic orders. Furthermore, some aging properties of these systems have been studied. Finally, some numerical examples are given to illustrate the proposed results.
ISSN:0269-9648
1469-8951
DOI:10.1017/S0269964821000425