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On relevation redundancy to coherent systems at component and system levels

Part of: Operations research and management science Survival analysis and censored data

Published online by Cambridge University Press:  09 June 2023

Chen Li Open the ORCID record for Chen Li [Opens in a new window]  and
Xiaohu Li Open the ORCID record for Xiaohu Li [Opens in a new window]
Chen Li*
Affiliation:
Tianjin University of Commerce
Xiaohu Li*
Affiliation:
Stevens Institute of Technology
*
*Postal address: School of Science, Tianjin University of Commerce, Tianjin 300134, China. Email address: lichenxm@hotmail.com
**Postal address: Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ 07030, USA. Email address: xli82@stevens.edu
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Abstract

Recently, the relevation transformation has received further attention from researchers, and some interesting results have been developed. It is well known that the active redundancy at component level results in a more reliable coherent system than that at system level. However, the lack of study of this problem with relevation redundancy prevents us from fully understanding such a generalization of the active redundancy. In this note we deal with relevation redundancy to coherent systems of homogeneous components. Typically, for a series system of independent components, we have proved that the lifetime of a system with relevation redundancy at component level is larger than that with relevation redundancy at system level in the sense of the usual stochastic order and the likelihood ratio order, respectively. For a coherent system with dependent components, we have developed a sufficient condition in terms of the domination function to the usual stochastic order between the system lifetime with redundancy at component level and that at system level.

Keywords

Coherent systemcopuladomination functionhazard rate orderlikelihood ratio orderseries systemusual stochastic order

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 104 - 120
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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