C&SA | Contents

Volume 60 >>> № 3 MAY — JUNE 2024

-->

DOI 10.34229/KCA2522-9664.24.3.12

UDC 519.21

O.O Kushnir¹, V.P. Kushnir²

¹ National University of Water Management and Natural Resources, Rivne, Ukraine

o.o.kushnir@nuwm.edu.ua;
kuchniroo@gmail.com

² National University of Water Management and Natural Resources, Rivne, Ukraine

v.p.kushnir@nuwm.edu.ua

ESTIMATION OF THE TIME-TO0FAILURE DISTRIBUTION FUNCTION IN A HIGHLY
RELIABLE N –1-OUT-OF-N : G REPAIRABLE SYSTEM IN THE CASE OF EXPONENTIAL
DISTRIBUTIONS OF WORKING PERIODS OF ALL ALTERNATING RENEWAL PROCESSES

Abstract. Some quantitative bounds on a convergence rate of the time-to-failure distribution function to an exponential distribution function in a highly reliable N –1-out-of-N : G repairable system are obtained in the case of exponential working periods of alternating renewal processes. The confident time to failure of this system is also bounded.

Keywords: alternating renewal process, N –1-out-of-N : G repairable system, Renyi’s theorem, semi-Markov process.

full text

REFERENCES

Korlat A.N., Kuznetsov V.N., Novikov M.M., Turbin A.F. Semi-Markov models of recoverable systems and queuing systems [in Russian]. Chisinau: Stintsa, 1991. 276 p.

Kuznetsov N.Yu. Limit distribution of the first moment of occurrence of a rare event in a system described by m independent recovery processes. Dokl. NAN USSR. 1979. N 1. P. 329–334.

Kartashov N.V. Inequalities in the Renyi theorem. Theory of Probability and Mathematical Statistics. 1992. N 45. P. 23–28.

Kushnir O.O., Kushnir V.P. Properties of highly reliable systems with protection in the case of Poisson renewal process. Theory of Probability and Mathematical Statistics. 2018. N 96. P. 127–132. https://doi.org/10.1090/tpms/1038.

UDC 519.21

ESTIMATION OF THE TIME-TO0FAILURE DISTRIBUTION FUNCTION IN A HIGHLY RELIABLE N –1-OUT-OF-N : G REPAIRABLE SYSTEM IN THE CASE OF EXPONENTIAL DISTRIBUTIONS OF WORKING PERIODS OF ALL ALTERNATING RENEWAL PROCESSES

REFERENCES

ESTIMATION OF THE TIME-TO0FAILURE DISTRIBUTION FUNCTION IN A HIGHLY
RELIABLE N –1-OUT-OF-N : G REPAIRABLE SYSTEM IN THE CASE OF EXPONENTIAL
DISTRIBUTIONS OF WORKING PERIODS OF ALL ALTERNATING RENEWAL PROCESSES