Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The reliability function defined by a failure rate which is a stochastic process with nonnegative and right continuous trajectories is presented in this paper. The reliability function with an at most countable state space semi-Markov failure rate process is investigated. A theorem concerning of equations for a conditional reliability function with a semi-Markov process as a failure rate is presented in this paper. The solutions of the proper renewal equations allow getting the reliability functions for the finite space semi-Markov random walk, for the Poisson process and for the Furry-Yule process as a failure rate.
Rocznik
Tom
Strony
209--216
Opis fizyczny
Bibliogr. 14 poz., wykr.
Twórcy
autor
- Polish Naval University, Gdynia, Poland
Bibliografia
- [1] Cinlar, E. (1969). Markov renewal theory. Adv. in Appl. Probab.1 123-187.
- [2] Feller, W. (1964). On semi-Markov prcesses. Proc. Nat. Acad. Sci. USA, 51, No 4, 653-659.
- [3] Grabski, F. (2002). Semi-Markov models of reliability and operation. Warszawa, IBS PAN, 2002, (in Polish)
- [4] Grabski, F. (2003). The reliability of an object with semi-Markov failure rate. Applied Mathematics and Computation 135, 1-16.
- [5] Grabski, F. (2011). Semi-Markov failure rate process. Applied Mathematics and Computation 217, 9956-9965.
- [6] Korolyuk, V.S. & Turbin, A.F. (1976) SemiMarkov Processes and Their Applications. Naukova Dumka, Kiev, (in Russian).
- [7] Kopocińska, I. & Kopociński, B. (1980). On system reliability under random load of elements. Aplicationes Mathematicae, XVII, 1, 5-14.
- [8] Kopocińska, I. (1984). The reliability of an element with alternating failure rate. Aplicationes Mathematicae, XVIII, 2, 187-194.
- [9] Korolyuk, V.S. & Turbin, A.F. (1982). Markov Renewal Processes in Reliability Problems. Naukova Dumka, Kiev, (in Russian).
- [10] Hassett, T.F., Dietrich, D.L. & Szidarovsky, F. (1995). Time-varying failure rates in the availability and reliability analysis of repairable systems. IEEE Transactions on reliability, Vol. 44, 155-160.
- [11] Limnios, N. & G. Oprisian, G. (2001). Semi-Markov Procesess and Reliability. Birkhauser, Boston, Basel, Berlin.
- [12] Ouhubi, B. & Limnios, N. (1998). Failure Rate Nonparametric Estimation in semi-Markov Systems. Proceedings of the 2nd International Symposium on Semi-Markov models: Theory and Applications. Universite de Technologie de Compiegne.
- [13] Silvestrov, D.C. (1980). Semi-Markov processes with a discrete state space. Sovetskoe Radio, Moskov. (in Russian).
- [14] Tanguy, C. (2009). Mean time to failure for periodic failure rate. Proceedings of SSARS 2009, 361-365.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-087ec004-bd56-42b6-850f-d59f72ac2167