Prediction Intervals Using Exceedances for an Additional Third-Stage Sample

Prediction intervals are extended to a third sampling stage involving the distribution of the t-th smallest value in a third-stage sample which exceeds the k-th smallest value in the second sample. Procedures and tables are given for two situations: A) The usual 2-stage prediction interval has been applied, and a third stage is now required; sample sizes are given for this problem. B) We know in advance that three stages will be necessary; the factors are given for the required procedure.