On some predictors of times to failure of censored items in progressively censored samples

In this article, we consider the problem of predicting times to failure of units censored in multiple stages in a progressively censored sample from an absolutely continuous population. The best linear unbiased predictors (BLUP), the maximum-likelihood predictors (MLP), and the conditional median predictors (CMP) are considered. The properties of MLP such as unbiasedness, consistency and efficiency are examined. The MLP or modified MLP (MMLP) are derived for exponential and extreme value populations. In addition, for these populations, the conditional distributions are used to derive the CMP. Comparison of different predictors are made with respect to mean squared prediction error (MSPE). Finally, some numerical examples are presented to illustrate all the prediction methods discussed here. Using simulation studies, prediction intervals are also generated for these examples.