Kayid, M.; Alshehri, M.A. Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level. Entropy2023, 25, 1033.
Kayid, M.; Alshehri, M.A. Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level. Entropy 2023, 25, 1033.
Kayid, M.; Alshehri, M.A. Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level. Entropy2023, 25, 1033.
Kayid, M.; Alshehri, M.A. Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level. Entropy 2023, 25, 1033.
Abstract
Recently, there has been growing interest in alternative measures of uncertainty, including
cumulative residual entropy. In this paper, we consider a mixed system consisting of n components,
assuming that all components are operational at time t. We use the system signature to calculate
the cumulative residual entropy of the mixed system’s remaining lifetime. This measure is a useful
criterion for assessing the predictability of a system’s lifetime. We study several results related to the
cumulative residual entropy of mixed systems, including expressions, limits, and order properties.
These results shed light on the behavior of the measure and provide insights into the predictability
of mixed systems. In addition, we propose a criterion for selecting a preferred system based on
the relative residual cumulative entropy. This criterion is closely related to the parallel system and
provides a practical way to choose the best system configuration. Overall, the present study of
cumulative residual entropy and the proposed selection criterion provide valuable insights into the
predictability of mixed systems and can be applied in various fields.
Keywords
coherent system; cumulative residual entropy; Shannon entropy; system signature
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
