Geodesic
Availability of a Repairable k-out-of-n: G System with Repair Times Arbitrarily Distributed
Serdica Mathematical Journal, Tome 40 (2014) no. 2, pp. 161-182.

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An k-out-of-n: G system is a system that consists of n components and works if and only if k components among the n work simultaneously. The system and each of its components can be in only one of two states: working or failed. When a component fails it is put under repair and the other components stay in the “working” state with adjusted rates of failure. After repair, a component works as new and its actual lifetime is the same as initially. If the failed component is repaired before another component fails, the (n − 1) components recover their initial lifetime. The lifetime and time of repair are independent. In this paper, we propose a technique to calculate the mean time of repair, the probability of various states of the system and its availability by using the theory of distribution. 2010 Mathematics Subject Classification: 90B25, 60K10.
Keywords: Availability, system, k-out-of-n, repairable 
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Gherda, Mebrouk; Boushaba, Mahmoud. Availability of a Repairable k-out-of-n: G System with Repair Times Arbitrarily Distributed. Serdica Mathematical Journal, Tome 40 (2014) no. 2, pp. 161-182. http://geodesic.mathdoc.fr/item/SMJ2_2014_40_2_a3/