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Mean First-Passage Times for a k-out-of-n System with Repair

Srinivas N. Iyer
The Journal of the Operational Research Society
Vol. 40, No. 10 (Oct., 1989), pp. 889-894
DOI: 10.2307/2583398
Stable URL: http://www.jstor.org/stable/2583398
Page Count: 6
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Mean First-Passage Times for a k-out-of-n System with Repair
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Abstract

Consider a k-out-of-n system where the lifetimes of the components are independent and identically distributed exponential (λ) random variables. Each component has its own repair facility, the repair times being independent and identically distributed exponential (μ) random variables, independent of the failure times. The mean operating time and mean repair time during the cycle between two successive breakdowns are found using renewal theory and the expression for the system availability. Using these, the mean first-passage times from any of the operating states of the system to the down state, and the mean first-passage times from any of the down states to the operating state are found recursively.

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