Life tests often require a long time to perform; therefore, engineers and statisticians seek to reduce the time to perform these tests. One way to shorten the failure time is to increase the stress level in the test units; in this case, the units fail earlier than when they are exposed to natural conditions. This method is called accelerated life testing. One common type of these tests is the step-by-step stress accelerated life test. In this method, the stress applied to the units under test is increased step by step and at predetermined times. The most important step in dealing with step-by-step stress testing is to optimize the design of this test. The purpose of optimizing the test design is to choose the best time to increase the stress level. In this article, the steps of performing a step-by-step stress test are first explained. Then, this test is applied to an exponential distribution. Since the life data are often not completely observed; We apply this model to type-1 censored data and optimize the test design by minimizing the asymptotic variance of the reliability estimate at time $xi$. Finally, the results are examined using simulation studies and real data. According to the sensitivity analysis, it is concluded that the optimal test design is stable.