One- and Two-Sided Tolerance Intervals for General Balanced Mixed Models and Unbalanced One-Way Random Models

Abstract

A tolerance interval, a statistical interval pertains to a specified proportion of a population, is an important statistical tool and widely used in various practical applications, such as plant or animal inbreeding, environmental monitoring and regulation, pharmaceutical engineering, process reliability studies, quality control, etc. In this talk, we develop procedures for one- and two-sided tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The procedures proposed are based on the concept of generalized pivotal quantities (GPQs) and are applicable to general mixed models provided balanced data is available. However, this study focuses on situations involving unbalanced data. Specific attention is given to the unbalanced one-way random model. It is shown that the use of GPQs allows the construction of the tolerance intervals of interest fairly straightforward. Some practical examples are given to illustrate the proposed procedures. Furthermore, detailed statistical simulation studies are conducted to evaluate their performance, showing that the proposed procedures can be recommended for practical use.