Two-sided tolerance intervals for balanced and unbalanced random effects models

A procedure for constructing two-sided beta-content, gamma-confidence tolerance intervals is proposed for general random effects models, in both balanced and unbalanced data scenarios. The proposed intervals are based on the concept of effective sample size and modified large sample methods for constructing confidence bounds on functions of variance components. The performance of the proposed intervals is evaluated via simulation techniques. The results indicate that the proposed intervals generally maintain the nominal confidence and content levels. Application of the proposed procedure is illustrated with a one-fold nested design used to evaluate the performance of a quantitative bioanalytical method.