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Keywords:
cold-standby redundant system; time to system failure; stationarystate probabilities
cold-standby redundant system; time to system failure; stationarystate probabilities
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.
References:
[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
[2] R. E. Barlow F. Proschan: Mathematical theory of reliability. J. Wiley, New York-London -Sydney (1965). MR 0195566
[3] B. V. Gnedenko, Ju. K. Beljajev A. D. Solovjev: Математические методы в теории надежности. Nauka, Moskva (1965). MR 0217823
[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.
[5] B. Kopociński: Outline of renewal and reliability theory. (Polish). Państwowe wydawnictwo naukowe, Warszawa (1973). MR 0423567
[6] V. S. Koroljuk A. F. Turbin: Полумарковские процессы и их приложения. Naukova dumka, Kijev (1976). MR 0420902
[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
[8] S. Osaki: On a two-unit standby redundant system with imperfect swichover. IEEE Trans. Reliab. R-21 (1972), 1, 20-24.
[9] S. Osaki T. Nakagawa: Bibliography for reliability and availability of stochastic systems. IEEE Trans. Reliab. R-25 (1976), 4, 284-286. MR 0403609
[10] P. R. Parthasarathy: Cost analysis for 2-unit systems. IEEE Trans. Reliab. R-28 (1979), 3, 268-269. Zbl 0411.62074
[11] D. Szász: A problem of two lifts. Ann. Prob. 5 (1977), 4, 550-559. DOI 10.1214/aop/1176995760 | MR 0461701
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