In life-testing experiments, it is often of interest to predict unobserved future failure times based on observed early failure times. A point best linear unbiased predictor (BLUP) has been developed in this context by Kaminsky and Nelson (J Am Stat Assoc 70:145–150, 1975). In this article, we develop joint BLUPs of two future failure times based on early failure times by minimizing the determinant of the variance–covariance matrix of the predictors. The advantage of applying joint prediction is demonstrated by using two real data sets. The non-existence of joint BLUPs in certain setups is also discussed.

中文翻译：

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阶次统计的 D 最优联合最佳线性无偏预测

在寿命测试实验中，根据观察到的早期故障时间预测未观察到的未来故障时间通常很有趣。Kaminsky 和 ​​Nelson (J Am Stat Assoc 70:145–150, 1975) 在此背景下开发了点最佳线性无偏预测器 (BLUP)。在本文中，我们通过最小化预测变量的方差-协方差矩阵的行列式，基于早期故障时间开发了两个未来故障时间的联合 BLUP。通过使用两个真实数据集证明了应用联合预测的优势。还讨论了某些设置中不存在联合 BLUP。