This expository paper presents theory for optimum plans for accelerated life tests for estimating a simple linear relationship between a stress and product life, which has a normal or lognormal distribution, when the data are to be analyzed before all test units fail. Standard plans with equal numbers of test units at equally spaced test stresses are presented and are compared with the optimum plans. While the optimllm plans may not always be robust enough in practice, they indicate that more test units should be run at low stress than at high stress. The plans are illustrated with a temperatllre-accelersted life test of an electrical insulation analyzed with the Arrhenius model.