One-sided tolerance interval in a two-way balanced nested model with mixed effects

In this paper we approach the construction of the both upper and lower tolerance limit in a two-way nested model with mixed effects in balanced data. In order to do so we proceed as Fonseca et al [1] did in order to derive the upper tolerance limit in a two-way nested model with mixed effects in unbalanced data, by using the generalized confidence interval idea earlier used by Krishnamoorthy and Mathew [2] to perform the construction of the upper tolerance limit in a one-way nested model with mixed or random effects model in balanced and unbalanced data. The underlying idea goes through the construction of an approximation for the quantile of the general pivotal quantity for a convinient parametric function.