AbstractA common problem in life testing is to demonstrate that the mean time to failure, θ, exceeds some minimum acceptable value, say θ1, with a given confidence coefficient γ. When this is true, it is said that “θ1has been demonstrated with a confidence γ”. In this paper a Sequential Bayes Procedure (SBP) for demonstrating (by means of. a probability statement) that θ exceeds θ1is presented. The SBP differs from the classical procedure in the sense that a prior distribution is assumed on the parameter θ, calling for a Bayesian approach. The procedure is based on the sequence of