D-optimal joint best linear unbiased prediction of order statistics

TL;DR

This paper develops joint BLUPs for predicting two future failure times in life-testing experiments, optimizing the covariance determinant, and demonstrates advantages with real data while discussing limitations.

Contribution

It introduces a novel joint BLUP approach for multiple future failure times, extending previous single prediction methods.

Findings

Joint BLUPs improve prediction accuracy in life-testing.

Application to real data shows practical benefits.

Non-existence conditions for joint BLUPs are identified.

Abstract

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 (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 a real data set. The non-existence of joint BLUPs in certain setups is also discussed.