Prediction of failure times of censored items for a simple step-stress model with hybrid censoring from the exponential distribution

In this article, the problem of predicting times to failure of units from the Exponential Distribution which are censored under a simple step-stress model is considered. We discuss two kinds of predictors - the maximum likelihood predictors (MLP) and the conditional median predictors (CMP) in the context of Type I and Type II hybrid censoring scheme (HCS). In order to illustrate the prediction methods we use some numerical examples. Furthermore, mean squared prediction error (MSPE) and prediction intervals are generated for these examples using simulation studies. MLP and the CMP are then compared with respect to the prediction interval for each type of censoring. Finally, we used a real data to apply the prediction methods developed in the article.