Reliability of a cold-standby redundant system with heterogeneous elements. P. 2. Approximate determination of reliability characteristics

The problem of approximately determining the reliability characteristics of a redundant cold-reserve system with unlimited recovery in a non-homogeneous case is considered. For the constructed semi-Markov model with a phase space of states of a general form, under the condition of “rapid” recovery of the system’s elements, the algorithm of asymptotic phase merging is applied, which makes it possible to obtain formulas for the approximate determination of steady-state reliability characteristics in a non-homogeneous case and to analyze their errors. In addition, an expression is obtained for the approximate calculation of the probability of failure-free operation of the system under consideration. The research results can be used to analyze the reliability of redundant radio engineering, information, energy, and some other systems at their design and operation stages.

1. Obzherin Yu. E., Sidorov S.M. Journal of Instrument Engineering, 2026, no. 7(69), pp. 569–582. (in Russ.)

2. Solov’ev A.D. Proc. of the USSR Academy of Sciences, Technical Cybernetics, 1970, no. 1, pp. 56–71.

3. Genis Y. Reliability: Theory & Appl., 2006, no. 3(1), pp. 31–47.

4. Korolyuk V.S., Turbin A.F. Protsessy markovskogo vosstanovleniya v zadachakh nadezhnosti sistem (Markov Recovery Processes in System Reliability Problems), Kiеv, 1982, 236 р. (in Russ.)

5. Korlat A.N., Kuznetsov V.N., Novikov M.I., Turbin A.F. Polumarkovskiye modeli vosstanavlivayemykh sistem i sistem massovogo obsluzhivaniya (Semi-Markov Models of Recoverable Systems and Queuing Systems), Kishinev, 1991, 276 р. (in Russ.)

6. Korolyuk V.S., Korolyuk V.V. Stochastic Models of Systems, Dordrech, Springer Science + Business Media, 1999, 185 p.

7. Korolyuk V.S., Limnios N. Stochastic systems in merging phase space, Imperial Coledge Press, World Scientific, 2005, 348 p.

8. Belyaev Yu.K., Bogatyirev V.A., Bolotin V.V. et. al. Nadezhnost' tehnicheskih system (Reliability of Technical Systems), Moscow, 1985, 608 p. (in Russ.)