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Optimal times of changing stress level for simple step-stress plans under a cumulative exposure model using the log-normal distribution are determined for a wide range of values of the parameters in the model. A table of optimal times of changing stress level for various model parameters values is obtained. A formula for optimal time of changing stress level is also estimated from the table. This paper provides an optimal life testing plan which will enable us to accurately estimate the 50th percentile of the life time of a product being tested without having to wait long time for the product to fail.