Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level
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 <i>n</i> components, assuming that all components are operational at time <i>t</i>. By utilizing th...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/7/1033 |
| _version_ | 1797589394919522304 |
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| author | Mohamed Kayid Mashael A. Alshehri |
| author_facet | Mohamed Kayid Mashael A. Alshehri |
| author_sort | Mohamed Kayid |
| collection | DOAJ |
| description | 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 <i>n</i> components, assuming that all components are operational at time <i>t</i>. By utilizing the system signature, we are able to compute the cumulative residual entropy of a mixed system’s remaining lifetime. This metric serves as a valuable tool for evaluating 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. |
| first_indexed | 2024-03-11T01:06:02Z |
| format | Article |
| id | doaj.art-c81626e7cb214d0b87a89576a9c2de95 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T01:06:02Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c81626e7cb214d0b87a89576a9c2de952023-11-18T19:13:45ZengMDPI AGEntropy1099-43002023-07-01257103310.3390/e25071033Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System LevelMohamed Kayid0Mashael A. Alshehri1Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi ArabiaDepartment of Quantitative Analysis, College of Business Administration, King Saud University, Riyadh 11362, Saudi ArabiaRecently, there has been growing interest in alternative measures of uncertainty, including cumulative residual entropy. In this paper, we consider a mixed system consisting of <i>n</i> components, assuming that all components are operational at time <i>t</i>. By utilizing the system signature, we are able to compute the cumulative residual entropy of a mixed system’s remaining lifetime. This metric serves as a valuable tool for evaluating 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.https://www.mdpi.com/1099-4300/25/7/1033coherent systemcumulative residual entropyShannon entropysystem signature |
| spellingShingle | Mohamed Kayid Mashael A. Alshehri Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level Entropy coherent system cumulative residual entropy Shannon entropy system signature |
| title | Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level |
| title_full | Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level |
| title_fullStr | Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level |
| title_full_unstemmed | Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level |
| title_short | Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level |
| title_sort | cumulative residual entropy of the residual lifetime of a mixed system at the system level |
| topic | coherent system cumulative residual entropy Shannon entropy system signature |
| url | https://www.mdpi.com/1099-4300/25/7/1033 |
| work_keys_str_mv | AT mohamedkayid cumulativeresidualentropyoftheresiduallifetimeofamixedsystematthesystemlevel AT mashaelaalshehri cumulativeresidualentropyoftheresiduallifetimeofamixedsystematthesystemlevel |