Failure time distributions for complex equipment

Abstract

Abstract The exponential distribution is inadequate as a failure time model for most components; however, under certain conditions (in particular, that component failure rates are small and mutually independent, and failed components are immediately replaced or perfectly repaired), it is applicable to complex repairable systems with large numbers of components in series, regardless of component distributions, as shown by Drenick in 1960. This result implies that system behavior may become simpler as more components are added. We review necessary conditions for the result and present some simulation studies to assess how well it holds in systems with finite numbers of components. We also note that Drenick's result is analogous to similar results in other systems disciplines, again resulting in simpler behavior as the number of entities in the system increases.