TY - JOUR
T1 - On relevation redundancy to coherent systems at component and system levels
AU - Li, Chen
AU - Li, Xiaohu
N1 - Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust.
PY - 2024/3/9
Y1 - 2024/3/9
N2 - 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.
AB - 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.
KW - Coherent system
KW - copula
KW - domination function
KW - hazard rate order
KW - likelihood ratio order
KW - series system
KW - usual stochastic order
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U2 - 10.1017/jpr.2023.31
DO - 10.1017/jpr.2023.31
M3 - Article
AN - SCOPUS:85161947122
SN - 0021-9002
VL - 61
SP - 104
EP - 120
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 1
ER -