Within the pharmaceutical industry it is common practice to transfer analytical methods from one laboratory to other laboratories. An experiment or interlaboratory study is performed to estimate the repeatability, the intermediate precision, and the reproducibility of the analytical method. These measures of precision are quantified by appropriate sums of variance components from an analysis of variance model describing the structure of the data. In the literature, several methods have been described for calculating approximate (closed-form) confidence intervals on sums of variance components, i.e., Welch, Satterthwaite, and modified large-sample (MLS). Comparisons between these methods have been performed for one-way and two-way classification analysis of variance models only. Interlaboratory studies though often need higher order classifications. Therefore, these methods for constructing confidence intervals are compared on the measures of precision from a specfic three-way classification analysis of variance model that is frequently used for method transfer studies. Using a simulation study, the coverage probability for these methods is evaluated in situations where variance components may be estimated negatively with the standard moment estimates and where either the standard moment estimates are adjusted to zero or remain unadjusted. The MLS method is superior to the other two methods in case the standard moment estimates are used. If the adjusted moment estimates are used, then the method of Satterthwaite performs similar to the MLS method for many settings of the variance components and sample sizes but much better for some particular settings. The method of Satterthwaite performs better than the method of Welch for all the selected settings of variance components and sample sizes, irrespective of the standard or adjusted moment estimates.