Reliability of 2-out-of-3 system considering number of spares and exchange time

The reliability of a simplified model of ractor instrumentation possessing redundancy in its system is studied. The unreliability is obtained for a 2-out-of-3 system with a limited number of spare units, for the case where the replacement of the failed unit by a spare unit is not instantaneous. Two methods for the solution are obtained. The results are then compared with that obtained from Jacobs' formula for a rate of false scrams, and the accuracy of Jacobs' formula is discussed. It is shown that Jacobs' formula can be used only when the duration of operation is larger than several times the reset time, which must be a constant. But in actuality this reset time depends on such factors as the number of spare units provided, and the time required for replacement.