On Optimal Redundancy

A complex system is to be placed in the field for a fixed period. During the period only the spares initially provided may be used to replace components that have failed. Independence of failures is assumed among the essential components considered. Given the cost of components, the number of like components of each type simultaneously operating, the length of operation scheduled for each component, the failure distributions of components, a general mathematical solution is obtained for the composition of the spare parts kit which maximizes assurance of continued operation during the period, subject to a fixed budget for spares. Explicit formulas are obtained in the case of exponential failure distributions, constructive procedures in the case of monotone likelihood ratio densities. Fortunately, the identical mathematical model is applicable in determining the optimal allocation of redundancy in designing system reliability under a weight or cost restraint.