Semi-Markovian Model of Control of Restorable System with Latent Failures ()
Abstract
Mathematical model of control of restorable system with latent failures has been built. Failures are assumed to be detected after control execution only. Stationary characteristics of system operation reliability and efficiency have been defined. The problem of control execution periodicity optimization has been solved. The model of control has been built by means of apparatus of semi-Markovian processes with a discrete-contin- uous field of states.
Share and Cite:
Y. Obzherin, A. Peschansky and Y. Boyko, "Semi-Markovian Model of Control of Restorable System with Latent Failures,"
Applied Mathematics, Vol. 2 No. 3, 2011, pp. 383-388. doi:
10.4236/am.2011.23046.
Conflicts of Interest
The authors declare no conflicts of interest.
References
|
[1]
|
D. I. Cho and M. Parlar, “A Survey of Maintenance Models for Multi-Unit Systems,” European Journal of Operational Research, Vol. 51, No. 2, 1991, pp. 1-23. doi:10.1016/0377-2217(91)90141-H
|
|
[2]
|
R. Dekker and R. A. Wildeman, “A Review of Multi- Component Maintenance Models with Economic Dependence,” Mathematical Methods of Operations Research, Vol. 45, No. 3, 1997, pp. 411-435. doi:10.1007/BF01194788
|
|
[3]
|
F. Beichelt and P. Franken, “Zuverlassigkeit und Instavphaltung,” Mathematische Methoden, VEB Verlag Technik, Berlin, 1983.
|
|
[4]
|
R. E. Barlow and F. Proschan, “Mathematical Theory of Reliability,” John Wiley & Sons, New York, 1965.
|
|
[5]
|
Y. E. Obzherin and A. I. Peschansky, “Semi-Markovian Model of Monotonous System Maintenance with Regard to Its Elements Deactivation and Age,” Applied Mathematics, Vol. 1, No. 3, 2010, pp. 234-243. doi:10.4236/am.2010.13029
|
|
[6]
|
V. S. Korolyuk and A. F. Turbin, “Markovian Restoration Processes in the Problems of System Reliability,” Naukova Dumka, Kiev, 1982.
|
|
[7]
|
V. M. Shurenkov, “Ergodic Markovian Processes,” Nauka, Moscow, 1989.
|