A Simple Repairable System with Warning Device
This paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/671756 |
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| _version_ | 1832567336806121472 |
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| author | Xiao Zhang Lina Guo |
| author_facet | Xiao Zhang Lina Guo |
| author_sort | Xiao Zhang |
| collection | DOAJ |
| description | This paper considers a simple repairable system with a warning device which can signal
an alarm when the system is not in good condition and a repairman who can have delayed-multiple
vacations. By using Markov renewal process theory and the
probability analysis method, the system is first described into a group of integrodifferential
equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution,
are studied by using the strongly continuous semigroup theory or C0 semigroup theory and the
spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes 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-ccd3cb686de74c88997cdfb60108e39e |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-ccd3cb686de74c88997cdfb60108e39e2025-02-03T01:01:47ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/671756671756A Simple Repairable System with Warning DeviceXiao Zhang0Lina Guo1Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, ChinaDepartment of Mathematics, Taiyuan University of Technology, Taiyuan 030024, ChinaThis paper considers a simple repairable system with a warning device which can signal an alarm when the system is not in good condition and a repairman who can have delayed-multiple vacations. By using Markov renewal process theory and the probability analysis method, the system is first described into a group of integrodifferential equations. Then the unique existence and asymptotic stability, especially the exponential stability of the system dynamic solution, are studied by using the strongly continuous semigroup theory or C0 semigroup theory and the spectrum theory. The reliability indices and some applications (such as the comparisons of some indexes 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/10.1155/2015/671756 |
| spellingShingle | Xiao Zhang Lina Guo A Simple Repairable System with Warning Device Journal of Function Spaces |
| title | A Simple Repairable System with Warning Device |
| title_full | A Simple Repairable System with Warning Device |
| title_fullStr | A Simple Repairable System with Warning Device |
| title_full_unstemmed | A Simple Repairable System with Warning Device |
| title_short | A Simple Repairable System with Warning Device |
| title_sort | simple repairable system with warning device |
| url | http://dx.doi.org/10.1155/2015/671756 |
| work_keys_str_mv | AT xiaozhang asimplerepairablesystemwithwarningdevice AT linaguo asimplerepairablesystemwithwarningdevice AT xiaozhang simplerepairablesystemwithwarningdevice AT linaguo simplerepairablesystemwithwarningdevice |