Point and Interval Estimation for a Simple Step- Stress Model with Random Stress-Change Time

In accelerated testing, the units are tested at varying stress levels. A special class of accelerated tests is step-stress test, that allows the experimenter to change the stress levels at pre-specified times during the experiment. It is observed that in the conventional step-stress testing, the parameters are not always estimable and even when the life time distributions are exponential, the exact confidence intervals are quite complicated. In this paper, we consider a simple step-stress model with a random stress-change time. In this set up the stress level changes at the time when a pre-specified number of failures take place. We derive the maximum likelihood estimators when the life time distributions are exponential and under the assumption of a cumulative exposure model. The joint distribution of the parameters is obtained. We provide the confidence intervals using the exact distribution and by two bootstrap methods. Bayes estimates and the corresponding credible intervals are also obtained. Monte Carlo simulations are performed to compare the performances of the different methods.