Two-Sided Tolerance Limits for Balanced Random-Effects ANOVA Models

In this article, we derive two-sided approximate β-content tolerance limits for multiway balanced random-effects models. We provide factors, obtained from numerical integration, that can be used to obtain β-content tolerance intervals. We describe methods for extending the results to nested models and discuss the use of the tabled tolerance factors for exact intervals for simple random samples when we have an independent estimate of the variance. We demonstrate the procedure with an experimental design used to evaluate the firing time precision in a high-explosives system.