The Weibull Process (a nonhomogeneous Poisson process with intensity r(t) = λβtβ−1) is considered as a stochastic model for the Duane (1964) reliability growth postulate. Under this model the mean time between failure (MTBF) for the system at time t is given by M(t) = [r(t)]−1. Small sample and asymptotic confidence intervals on M(t) are discussed for failure- and time-truncated testing. Tabled values to compute the confidence intervals and numercial examples illustrating these procedures are presented.