Stability Analysis of a Repairable System with Warning Device and Repairman Vacation
This paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/674191 |
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| _version_ | 1832560471891247104 |
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| author | Yangli Ren Lina Guo Lingling Zhang |
| author_facet | Yangli Ren Lina Guo Lingling Zhang |
| author_sort | Yangli Ren |
| collection | DOAJ |
| description | This paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the
probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and uniqueness as well as regularity of the system dynamic solution are discussed with the functional analysis method. Further, the asymptotic stability, especially the exponential stability of the system dynamic solution, is studied by using the strongly continuous semigroup theory or C0 semigroup theory. The reliability indices and some applications (such as the comparisons of indices and profit of systems with and without warning device), as well as numerical examples, are presented at the end of the paper. |
| format | Article |
| id | doaj-art-345e45346d734294b25317f920fca804 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-345e45346d734294b25317f920fca8042025-02-03T01:27:32ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/674191674191Stability Analysis of a Repairable System with Warning Device and Repairman VacationYangli Ren0Lina Guo1Lingling Zhang2Department of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaThis paper considers a simple repairable system with a warning device and a repairman who can have delayed-multiple vacations. By Markov renewal process theory and the probability analysis method, the system is first transformed into a group of integrodifferential equations. Then, the existence and uniqueness as well as regularity of the system dynamic solution are discussed with the functional analysis method. Further, the asymptotic stability, especially the exponential stability of the system dynamic solution, is studied by using the strongly continuous semigroup theory or C0 semigroup theory. The reliability indices and some applications (such as the comparisons of indices and profit of systems with and without warning device), as well as numerical examples, are presented at the end of the paper.http://dx.doi.org/10.1155/2013/674191 |
| spellingShingle | Yangli Ren Lina Guo Lingling Zhang Stability Analysis of a Repairable System with Warning Device and Repairman Vacation Journal of Function Spaces and Applications |
| title | Stability Analysis of a Repairable System with Warning Device and Repairman Vacation |
| title_full | Stability Analysis of a Repairable System with Warning Device and Repairman Vacation |
| title_fullStr | Stability Analysis of a Repairable System with Warning Device and Repairman Vacation |
| title_full_unstemmed | Stability Analysis of a Repairable System with Warning Device and Repairman Vacation |
| title_short | Stability Analysis of a Repairable System with Warning Device and Repairman Vacation |
| title_sort | stability analysis of a repairable system with warning device and repairman vacation |
| url | http://dx.doi.org/10.1155/2013/674191 |
| work_keys_str_mv | AT yangliren stabilityanalysisofarepairablesystemwithwarningdeviceandrepairmanvacation AT linaguo stabilityanalysisofarepairablesystemwithwarningdeviceandrepairmanvacation AT linglingzhang stabilityanalysisofarepairablesystemwithwarningdeviceandrepairmanvacation |