In studying the waiting times between failures of a series system whose components fail independently and are replaced upon failure, it is well known that for large systems in time equilibrium, the distribution of waiting times is approximately exponential. Correction terms are available to account for the finite number of components. Here, correction terms are developed for the finite age of the system as well. Also numerical studies are presented indicating the magnitude of the error in reliability predictions based on the assumption of time equilibrium when system age is really finite.