Joint Prediction for Future Failures Times Under Type-II Censoring

The construction of prediction sets (or regions) for future failure times based on a type-II censored sample from the exponential distribution is investigated. Based on the distribution of the sum of independent exponential variables with different parameters, we obtain the distribution of the required pivotal quantities in order to find the prediction regions. Balanced prediction sets are first derived. A constrained optimization problem is then formulated and solved to determine the prediction region with minimal area. A Monte Carlo simulation study is carried out to compare the performance of the proposed prediction sets. Two real data examples are provided and analyzed to illustrate the methods presented. Finally, some applications and extensions of the results are discussed.