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Based on progressive first-failure censoring, step-stress partially accelerated life tests are considered when the lifetime of a product follows Weibull distribution. The maximum likelihood estimates (MLEs) are obtained for the distribution parameters and the acceleration factor. In addition, asymptotic variance and covariance matrix of the estimators are given. Furthermore, confidence intervals of the estimators are presented. The optimal stress change time for the step-stress partially accelerated life test is determined by minimizing the asymptotic variance of MLEs of the model parameters and the acceleration factor. Simulation results are carried out to study the precision of the MLEs for the parameters involved.

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