Consider the case of a single test unit which must be tested at some level of test stress. Suppose that the test stress level is free to be determined, and that only the survival or nonsurvival of the unit is observed. It is assumed that the unit is designed to withstand a known and specified design stress level. A Bayesian model is developed for determining the required level of test stress which maximizes the expected probability of survival at the design stress level. Engineering experience from similar past tests on similar units is used to fit the model. A practical application illustrates the method. The sensitivity of the procedure to changes in the parameters used in fitting the model is also examined.