In this paper, the problem of predicting times to failure of units censored in multiple stages of progressively hybrid censoring for the proportional hazards family is considered. We discuss different classical predictors. The best unbiased predictor (BUP), the maximum likelihood predictor (MLP) and conditional median predictor (CMP) are all derived. As an example, the obtained results are computed for exponential distribution. A numerical example is presented to illustrate the prediction methods discussed here. Using simulation studies, the predictors are compared in terms of bias and mean squared prediction error (MSPE).

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