Tsallis Entropy for the Past Lifetime Distribution with Application
A fundamental factor in relevant applications is the predictability of the life cycle of a coherent system consisting of more than one component. In this context, we examine how entropy can be applied to evaluate the degree of predictability. In particular, in order to calculate the Tsallis entropy...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/12/8/731 |
| _version_ | 1797585530029867008 |
|---|---|
| author | Mohamed Kayid Mashael A. Alshehri |
| author_facet | Mohamed Kayid Mashael A. Alshehri |
| author_sort | Mohamed Kayid |
| collection | DOAJ |
| description | A fundamental factor in relevant applications is the predictability of the life cycle of a coherent system consisting of more than one component. In this context, we examine how entropy can be applied to evaluate the degree of predictability. In particular, in order to calculate the Tsallis entropy of the past life, we consider a scenario in which all components of the system fail at a given time <i>t</i> and use the system signature to calculate the Tsallis entropy of the past life. We examine a number of analytical results, e.g., expressions, thresholds and orders for the measure at issue in our study. The results may provide insights into the predictability of a coherent system’s life cycle. |
| first_indexed | 2024-03-11T00:07:26Z |
| format | Article |
| id | doaj.art-66ca64c0c9a24024b1eb2839ec892f25 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T00:07:26Z |
| publishDate | 2023-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-66ca64c0c9a24024b1eb2839ec892f252023-11-19T00:14:22ZengMDPI AGAxioms2075-16802023-07-0112873110.3390/axioms12080731Tsallis Entropy for the Past Lifetime Distribution with ApplicationMohamed 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 ArabiaA fundamental factor in relevant applications is the predictability of the life cycle of a coherent system consisting of more than one component. In this context, we examine how entropy can be applied to evaluate the degree of predictability. In particular, in order to calculate the Tsallis entropy of the past life, we consider a scenario in which all components of the system fail at a given time <i>t</i> and use the system signature to calculate the Tsallis entropy of the past life. We examine a number of analytical results, e.g., expressions, thresholds and orders for the measure at issue in our study. The results may provide insights into the predictability of a coherent system’s life cycle.https://www.mdpi.com/2075-1680/12/8/731coherent systempast Tsallis entropyShannon differential entropysystem signature |
| spellingShingle | Mohamed Kayid Mashael A. Alshehri Tsallis Entropy for the Past Lifetime Distribution with Application Axioms coherent system past Tsallis entropy Shannon differential entropy system signature |
| title | Tsallis Entropy for the Past Lifetime Distribution with Application |
| title_full | Tsallis Entropy for the Past Lifetime Distribution with Application |
| title_fullStr | Tsallis Entropy for the Past Lifetime Distribution with Application |
| title_full_unstemmed | Tsallis Entropy for the Past Lifetime Distribution with Application |
| title_short | Tsallis Entropy for the Past Lifetime Distribution with Application |
| title_sort | tsallis entropy for the past lifetime distribution with application |
| topic | coherent system past Tsallis entropy Shannon differential entropy system signature |
| url | https://www.mdpi.com/2075-1680/12/8/731 |
| work_keys_str_mv | AT mohamedkayid tsallisentropyforthepastlifetimedistributionwithapplication AT mashaelaalshehri tsallisentropyforthepastlifetimedistributionwithapplication |