On the Uncertainty Properties of the Conditional Distribution of the Past Life Time
For a given system observed at time <i>t</i>, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are <i>n</i> components that have all failed at time <i>t</i>. To assess the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/6/895 |
| _version_ | 1797594921071280128 |
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| author | Mohamed Kayid Mansour Shrahili |
| author_facet | Mohamed Kayid Mansour Shrahili |
| author_sort | Mohamed Kayid |
| collection | DOAJ |
| description | For a given system observed at time <i>t</i>, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are <i>n</i> components that have all failed at time <i>t</i>. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system’s life-time, which may be useful in a number of practical applications. |
| first_indexed | 2024-03-11T02:29:33Z |
| format | Article |
| id | doaj.art-3391a53fd2e64a5986f9e2a8021b10d9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:29:33Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3391a53fd2e64a5986f9e2a8021b10d92023-11-18T10:17:56ZengMDPI AGEntropy1099-43002023-06-0125689510.3390/e25060895On the Uncertainty Properties of the Conditional Distribution of the Past Life TimeMohamed Kayid0Mansour Shrahili1Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaFor a given system observed at time <i>t</i>, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are <i>n</i> components that have all failed at time <i>t</i>. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system’s life-time, which may be useful in a number of practical applications.https://www.mdpi.com/1099-4300/25/6/895coherent systempast entropyShannon differential entropysystem signature |
| spellingShingle | Mohamed Kayid Mansour Shrahili On the Uncertainty Properties of the Conditional Distribution of the Past Life Time Entropy coherent system past entropy Shannon differential entropy system signature |
| title | On the Uncertainty Properties of the Conditional Distribution of the Past Life Time |
| title_full | On the Uncertainty Properties of the Conditional Distribution of the Past Life Time |
| title_fullStr | On the Uncertainty Properties of the Conditional Distribution of the Past Life Time |
| title_full_unstemmed | On the Uncertainty Properties of the Conditional Distribution of the Past Life Time |
| title_short | On the Uncertainty Properties of the Conditional Distribution of the Past Life Time |
| title_sort | on the uncertainty properties of the conditional distribution of the past life time |
| topic | coherent system past entropy Shannon differential entropy system signature |
| url | https://www.mdpi.com/1099-4300/25/6/895 |
| work_keys_str_mv | AT mohamedkayid ontheuncertaintypropertiesoftheconditionaldistributionofthepastlifetime AT mansourshrahili ontheuncertaintypropertiesoftheconditionaldistributionofthepastlifetime |