A model resembling the Barlow-Scheuer reliability growth model [I] is examined from a Bayesian perspective. A Dirichlet prior distribution is assumed on the three parameters of the model, i.e. the probability of an inherent failure, the probability of an assignable-cause failure, and the probability of success. The model assumes that a subsystem is tested in independent stages. At each stage, the posterior distribution is a Dirichlet distribution, or a mixture of Dirichlet distributions, depending on whether the investigator can identify with certainty which of the assignable-failure causes are removed when those discovered during testing are corrected. Methodology is developed for estimating reliability at the end of each stage of testing and for obtaining lower and upper bounds for system reliability. The Barlow-Scheuer data are reexamined using the approach developed herein.