Design and Analysis of Step Stress Accelerated Life Tests for Censored Data}

Life testing often is consuming a very long time for testing. Therefore, the engineers and statisticians are looking for some approaches to reduce the running time. There is a recommended method for reducing the time of failure, such that the stress level of the test units will increase, and then they will fail earlier than normal operating conditions. These approaches are called accelerated life tests. One of the most common tests is called the step stress accelerated life test. In this procedure, the stress applied to the units under the test is increased step by step at a predetermined time. The most important aspect to deal with the step stress model is the optimization of test design. In order to optimize the test plan, the best time to increase the level of stress should be chosen. In this paper, at first the step stress testing described. Then, this test is used for exponential lifetime distribution. Since life data are often not complete, this model is applied to type I censored data. By minimizing the asymptotic variance of the maximum likelihood estimator of reliability at time $xi$, the optimal test plan will be obtained. Finally, the simulation studies and one real data are discussed to illustrate the results. A sensitivity analysis shows that the proposed optimum plan is robust.