Prediction intervals for Weibull observations, based on early-failure data

Let n similar components with Weibull lives be put on life-test simultaneously, and let the first r failures be observed. A prediction interval for failure-time X_k, 0<r<k⩽n, is constructed. An explicit formula is obtained for computing quantiles of a relevant pivotal statistic. Prediction intervals based on various estimators of parameters and methods are compared. The results can be used to predict the failure-time of a k-out-of-n:F system