Optimal allocation of change points in simple step-stress experiments under Type-II censoring

In simple step-stress experiments under Type-II censoring with the cumulative exposure model and exponentially distributed lifetimes, maximum likelihood estimates (MLE) of the expected lifetimes may not exist due to the absence of failure times either before or after the stress change point. For this reason, when planning a step-stress experiment, the change point could be chosen so as to minimize the probability of non-existence of the MLE. These non-existence probabilities are examined and compared in the one- as well as the two-sample situations. Moreover, the optimal allocations of the change points are discussed and the effects of the use of non-optimal choices for the change points are assessed.