Reliability of Spare Part Support for a Complex System with Repair

In this paper an expression is derived for the probability that a given number of spares for each element of a complex system will be sufficient to ensure continued operation without requiring a spare (for replacement of a failed part) when none is available. Each part of the system being considered is subject to failure according to Poisson statistics, and may be subject to repair in some fixed time. The probability (that the number of spares will be sufficient) for nonreparable parts is obtained as a special case of the result for reparable parts. The probabilities are obtained for a single part by the construction of an artificial model, which differs from the case being considered, allowing the deviation to shrink to zero. Samples of the results obtained are included for several values of the various parameters. The results are generalized to include a variety of parts, both identical and different, and to include the effects of passive redundancy.