Testing for the validity of the assumptions in the exponential step-stress accelerated life-testing model

In the application of the exponential step-stress accelerated life-testing model, there are usually three assumptions required: (1) for any stress level, the lifetime distribution of a test unit is exponential; (2) for any stress level, the mean life of a test unit is a log-linear function of stress; (3) a cumulative exposure model holds. This paper explores the validity of assumptions 1 and 3. It is proved that assumption 3 is unnecessary to the exponential step-stress accelerated life-testing model. A test statistic is proposed to test the validity of the assumptions 1. The null distribution of the test statistic is derived. A Monte Carlo simulation is given to study the power of the proposed test procedure. Finally, an example is given to illustrate the proposed test procedure.