A statistical model for step-stress accelerated life test is motivated from the point of view that a change of the stress has a multiplicative effect on the failure rate function over the remaining life.Properties of the proposed model, including an interpretation in terms of the conditional reliability, and relationships with the existing models are discussed. For the parametric setting of a Weibull family representing the life distribution under a constant stress, maximum likelihood estimation of the parameters is investigated and the Fisher information matrix is derived. The proposed model is found to have certain analytical advantages over the cumulative exposure model that is commonly used in step-stress analysis. An extension of the model to include a regression structure and inferences for life under the use condition stress are briefly discussed.