Availability of an n-Spare System with a Single Repair Facility

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Abstract
The availability of a repairable system having one operating unit supported by n standby units is analyzed. The units have an exponential failure time distribution and the failed units are repaired, one at a time, with a general repair time distribution. An asymptotic formula of the stationary availability is derived, and is shown to give exact results for exponential repair times. Numerical examples show that the asymptotic formula gives a good approximation even for small n.