Prediction on the basis of censored data has an important role in many fields. This paper develops a non-Bayesian two-sample prediction based on a progressive Type-II right censoring scheme. We obtain the maximum likelihood (ML) prediction in the Weibull distribution. The Weibull distribution is considered to obtain the ML predictor (MLP) and the predictive ML estimators of the s-th order statistic in a future random sample Y_s drawn independently from the parent population, for an arbitrary progressive censoring scheme. To reach this aim, we present two ML prediction methods namely the EM algorithm and the approximate ML prediction. We compare the performances of the different methods of ML prediction by Monte Carlo simulation with respect to biases and mean square prediction errors (MSPEs) of the MLPs of Y_s.
