A system reliability analysis for stand-by spares with non-zero unpowered failure rates

Equations which define the reliability of n-fold parallel systems with stand-by spares, and triply redundant, majority-voting systems with stand-by spares have been derived. The stand-by spares have been assumed to have a non-zero failure rate while in the stand-by mode. A Monte Carlo system simulation has been generated and the results compared to the theoretical reliability predictions. A comparison of these two stand-by configurations is also presented for three through six total units.