| Title:
|
Analysis of a two-unit standby redundant system with three states of units (English) |
| Author:
|
Lešanovský, Antonín |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
27 |
| Issue:
|
3 |
| Year:
|
1982 |
| Pages:
|
192-208 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A cold-standby redundant system with two identical units and one repair facility is considered. Units can be in three states> good (I), degraded (II), and failed (III). We suppose that only the following state-transitions of a unit are possible: $I\rightarrow II, II\rightarrow III, II\rightarrow I, III\rightarrow I$. The repair of a unit of the type $II \rightarrow I$ can be interpreted as a preventive maintenance. Its realization depends on the states of both units. Several characteristics of the system (probabilities, distribution functions or their Laplace-Stieltjes transforms and mathematical expectations) are derived, e.g. time to system failure, time of non-operating period of the system and stationary-state probabilities of the couple of units of the system. (English) |
| Keyword:
|
cold-standby redundant system |
| Keyword:
|
time to system failure |
| Keyword:
|
stationarystate probabilities |
| MSC:
|
60K10 |
| MSC:
|
60K20 |
| MSC:
|
62N05 |
| MSC:
|
90B25 |
| idZBL:
|
Zbl 0485.60085 |
| idMR:
|
MR0658002 |
| DOI:
|
10.21136/AM.1982.103962 |
| . |
| Date available:
|
2008-05-20T18:19:13Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/103962 |
| . |
| Reference:
|
[1] K. Arndt P. Franken: Construction of a class of stationary processes with applications in reliability.Zastosowania matematyki 16 (1979), 3, 319-393. MR 0534130 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[4] В. V. Gnedenko M. Dinič, Ju. Nasr: O надежности дублированной системы с восстановлением и профилактическим обслуживанием.Izv. AN SSSR, Techn. Kibernet. (1975), 1, 66-11. |
| Reference:
|
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| Reference:
|
[6] V. S. Koroljuk A. F. Turbin: Полумарковские процессы и их приложения.Naukova dumka, Kijev (1976). MR 0420902 |
| Reference:
|
[1] T. Nakagawa S. Osaki: Stochastic behaviour of a two-unit standby redundant system.INFOR Canad. J. Oper. Res. and Infor. Proc. 12 (1974), 1, 66-10. MR 0433630 |
| Reference:
|
[8] S. Osaki: On a two-unit standby redundant system with imperfect swichover.IEEE Trans. Reliab. R-21 (1972), 1, 20-24. |
| Reference:
|
[9] S. Osaki T. Nakagawa: Bibliography for reliability and availability of stochastic systems.IEEE Trans. Reliab. R-25 (1976), 4, 284-286. MR 0403609 |
| Reference:
|
[10] P. R. Parthasarathy: Cost analysis for 2-unit systems.IEEE Trans. Reliab. R-28 (1979), 3, 268-269. Zbl 0411.62074 |
| Reference:
|
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| . |
