Reliability of a System Having Standby Spare Plus Multiple-Repair Capability

Abstract

The reliability of a system having two identical and repairable units, one of which is operating while the other is in inactive standby, is treated. It is assumed that each unit has independent exponentially distributed failure times and independent gamma distributed repair times. The failure rate is λ, and the mean time to repair is τ. Formulas are derived which express system reliability and expected time to system failure, specifically, as a function of the capability for one repair, two repairs, and so on. Results are presented in graphical form. Important conclusions are: 1) the benefit of repair capability is negligible when λτ > 0.5; 2) the choice of the repair time distribution does not influence the results when λτ < 0.2; and 3) the effect of repair capability is comparable to that of additional standby units when λτ < 0.01.