A Journal "Theory of Probability and Mathematical Statistics"
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970


Archive

About   Editorial Board   Contacts   Template   Publication Ethics   Peer Review Process   Special Issues   History  

Theory of Probability and Mathematical Statistics



A STUDY OF CHARACTERISTICS OF A HIGHLY RELIABLE SYSTEM WITH PROTECTION ASSUMING THAT THE RENEWAL PROCESS IS POISSON

O. O. KUSHNIR, V. P. KUSHNIR

Download PDF

Abstract: We assess reliability characteristics of a highly reliable system of protection assuming that the renewal process is Poisson.

Keywords: процес відновлення, альтернуючий процес, система із захистом, теорема Реньї, напівмарковський процес.

Bibliography:
1. N. V. Kartashov, Inequalities in the Renyi theorem, Teor. Veroyatnost. Mat. Stat. 45 (1991), 27-33; English transl. in Theory Probab. Math. Statist. 45 (1992), 23-28.
2. V. S. Korolyuk, Stochastic Models of Systems, Lybid' , Kyiv, 1993. (Ukrainian)
3. O. O. Kushnir, A study of a highly reliable system with protection by the Renyi theorem, Teor. Imovir. Mat. Stat. 55 (1996), 117-124; English transl. in Theory Probab. Math. Statist. 55 (1997), 121-128.
4. O. O. Kushnir, A quantitative lower bound for the expected value of the failure time of a highly reliable system with protection in a nonstationary regime, Teor. Imovir. Mat. Stat. 61 (1999), 91-96; English transl. in Theory Probab. Math. Statist. 61 (2000), 95-100.
5. O. O. Kushnir, A logarithmic lower bound for the expected value of the time of failure-free operation of a highly reliable system with protection in a nonstationary mode, Teor. Imovir. Mat. Stat. 65 (2001), 104109; English transl. in Theory Probab. Math. Statist. 65 (2002), 115-121.
6. D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab. 8 (1980), no. 3, 615-621.
7. A. Ya. Khinchin, Works on Mathematical Queueing Theory, Fizmatgiz, Moscow, 1963. (Russian)