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Renewal theory concerns itself with the replacement of randomly failing parts. In the simplest case we have a one component system which is kept running continuously by replacing a failed component at the instant of failure with an identical “new” component. The random variable N(t) = the number of failures (or replacements) to time t is then of interest in many types of reliability analysis. In this paper the distribution of N(t) is considered when the underlying failure law is a Weibull distribution. Tables of the mean and standard deviation of N(t) for various values of the Weibull slope parameter are presented. Applications to warranty and spare parts analyses are also noted.