Abstract
We determine the stationary distribution of the embedded Markov chain of semimarkov processes that are supporting for a family of them describing the functioning of systems with a replenishable reserve time. The results obtained are used to give an approximate computation of the time to failure of a system with back-up and a large amount of replenishable reserve time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
G. N. Cherkesov,Reliability of Technical Systems with Surplus Time [in Russian], Soviet Radio, Moscow (1974).
B. P. Kredentser,Predicting the Reliability of Systems with Surplus Time [in Russian], Naukova Dumka, Kiev (1978).
Yu. E. Obzherin, “A Markov renewal process for systems with replenishable reserve time,” in:Analytic Methods of the Theory of Probability [in Russian], Inst. Matem. Akad. Nauk UkrSSR (1983), pp. 83–90.
V. S. Korolyuk and A. F. Turbin,Markov Renewal Processes in System Reliability Problems [in Russian], Naukova Dumka, Kiev (1982).
V. S. Korolyuk and A. F. Turbin,Semimarkov Processes and their Applications [in Russian], Naukova Dumka, Kiev (1976).
Author information
Authors and Affiliations
Additional information
Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 95–101.
Rights and permissions
About this article
Cite this article
Obzherin, Y.E., Skatkov, A.V. On the time to failure of systems with large replenishable reserve time. J Math Sci 57, 3429–3432 (1991). https://doi.org/10.1007/BF01880213
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01880213