Point and Interval Estimation for a Simple Step-Stress Model with Type-II Censoring

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress levels, such as temperature, voltage, and load, on the lifetimes of experimental units. Accelerated testing allows the experimenter to increase these stress levels to obtain information on the parameters of the life distributions more quickly than would be possible under normal operating conditions. A special class of accelerated tests are step-stress tests that allow the experimenter to increase the stress levels at fixed times during the experiment. In this article, we consider the simple step-stress model under Type-II censoring. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained through the use of conditional moment-generating functions. We also derive confidence intervals for the parameters using these exact distributions, asymptotic distributions, and the parametric bootstrap method, and assess their performance through a Monte Carlo simulation study.