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This paper considers optimal designs of step-stress accelerated life tests in which each lognormally-distributed test item is first run at low stress, and if it does not fail for a specified time, then it is run at high stress until a predetermined censoring time. It is assumed that a log-linear relation exists between the lognormal location parameter and stress, and that a cumulative exposure model for the effect of changing stress holds. The optimum stress change point minimizes the asymptotic variance of maximum likelihood estimator of a specified percentile at design stress. For selected values of the design parameters, the optimum plans are tabulated. Designs of high-to-low step-stress accelerated life tests (ALTs) in which each item is first run at high stress and then at low stress, and the optimality criterion of minimizing the generalized asymptotic variance of maximum likelihood estimators of model parameters, are also considered. The effects of the incorrect pre-estimates of the design parameters are investigated.

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