Availability calculations with exhaustible spares

Many systems rely solely on the spares they carry to fulfil their missions. The authors develop relatively simple equations for the availability of a system with exhaustible spares. The equations are conservative but, for a large system, are more tractable than simulation or the exact approach based on Markov theory. The equations are useful for tradeoff or sensitivity analysis. Given various complements of spares, system availability can be calculated, or the optimal selection of spares can be determined. Since the equations conservatively approximate system availability if the system consists of several types of units in series, the equations can be used to determine if a system meets its availability requirement. If the calculated system availability is less than the requirement, spares could be added or more exact techniques could be applied. Because of various simplifying assumptions, the equations are most exact when repair time is small compared to mission time and when k is close to n for k-out-of-n:G systems