Exact Inference and Optimal Censoring Scheme for a Simple Step-Stress Model Under Progressive Type-II Censorig

In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment in order to obtain information on the parameters of the life distribution more quickly than under normal operating conditions. In this article, we consider a simple step-stress model under the exponential distribution when the available data are progressively Type-II censored. 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 then construct confidence intervals for the parameters using these exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance through a Monte Carlo simulation study. Next, we investigate optimal progressive censoring schemes as well as optimal time for change of stress level based on the simple step-stress model. Finally, we present two examples to illustrate all the methods of inference discussed here.