Usually,for high reliability products the production cost is high and the lifetime is much longer, which may not be observable within a limited time. In this paper, all accelerated experiment is employed in which the lifetime follows all exponential distribution with the failure rate being related to the accelerated factor exponentially. The underlying parameters are also assumed to have the exponential prior distributions. A Bayesian zero-failure reliability demonstration test is conducted to design forehand the minimum sample size and testing length subject to a certain specified reliability criterion. Probability of passing the test design as well as predictive probability for additional experiments is also derived. Sensitivity analysis of the design is investigated by a simulation study. Copyright (C) 2009 John Wiley & Sons, Lid.