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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| Published in | Probability in the engineering and informational sciences Vol. 37; no. 1; pp. 1 - 28 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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New York, USA
Cambridge University Press
01.01.2023
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| Abstract | 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. |
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| AbstractList | 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. 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. |
| Author | Sahoo, Tanmay Hazra, Nil Kamal |
| Author_xml | – sequence: 1 givenname: Tanmay surname: Sahoo fullname: Sahoo, Tanmay email: nilkamal@iitj.ac.in organization: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan 342037, India. E-mail: nilkamal@iitj.ac.in – sequence: 2 givenname: Nil Kamal orcidid: 0000-0003-3210-6101 surname: Hazra fullname: Hazra, Nil Kamal email: nilkamal@iitj.ac.in organization: Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan 342037, India. E-mail: nilkamal@iitj.ac.in |
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| Keywords | Coherent system 60E15 Stochastic orders Archimedean copula 90B25 r-out-of-n system Stochastic agings |
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| Snippet | 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... |
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| SubjectTerms | Aging Lifetime Random variables |
| Title | Ordering and aging properties of systems with dependent components governed by the Archimedean copula |
| URI | https://www.cambridge.org/core/product/identifier/S0269964821000425/type/journal_article https://www.proquest.com/docview/2766326874 |
| Volume | 37 |
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