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.