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Stability analysis of a standby system with an unreliable server and switching failure.
- Source :
-
IMA Journal of Applied Mathematics . Apr2022, Vol. 87 Issue 2, p207-230. 24p. - Publication Year :
- 2022
-
Abstract
- This paper is devoted to analysing stability of a standby system with an unreliable server and switching failure, where both the time-to-repair of units and the time-to-repair of server follow general distributions. By employing $C_0$ semigroup theory, we show that time-dependent solution of the system converges to steady-state solution under a rather mild condition. Further, if component' repair rate and server's repair rate satisfy a reasonable assumption, then the system is exponentially stable. Based on the above theoretical foundation, some steady-state reliability indices are obtained and total expected profit function per unit time is developed. Finally, a sensitivity analysis with numerical illustrations is also provided. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02724960
- Volume :
- 87
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- IMA Journal of Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 157486086
- Full Text :
- https://doi.org/10.1093/imamat/hxac004