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

Part of: Distribution theory - Probability Operations research and management science

Published online by Cambridge University Press:  17 September 2021

Tanmay Sahoo  and
Nil Kamal Hazra Open the ORCID record for Nil Kamal Hazra [Opens in a new window]
Tanmay Sahoo
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan 342037, India. E-mail: nilkamal@iitj.ac.in
Nil Kamal Hazra
Affiliation:
Department of Mathematics, Indian Institute of Technology Jodhpur, Karwar, Rajasthan 342037, India. E-mail: nilkamal@iitj.ac.in
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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.

Keywords

Archimedean copulaCoherent systemr-out-of-n systemStochastic agingsStochastic orders

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 60E15: Inequalities; stochastic orderings
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 1 - 28
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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