A Tolerance Interval for Unbalanced One-Way Random Effects Models
Date Issued
2005-07-31
Date
2005-07-31
Author(s)
DOI
932118M002009
Abstract
Statistical tolerance intervals are useful in practical applications in Engineering,
Pharmaceutical industries, and many other areas. Construction of tolerance intervals for
univariate distributions has been extensively studied, particularly for exponential family
distributions such as normal, lognormal, exponential etc. An excellent review of these
procedures and their applications are given in Hahn and Meeker (1991). However, tolerance
intervals have not been explored in detail for more complex situations. Most of the papers on
the tolerance interval problem have concentrated on the balanced one-way random effects
model. The reader may refer to Lemon (1977), Mee and Owen (1983), Mee (1984), and
Vangel (1992) among others. Recently, Liao and Iyer (2003) have developed a tolerance
interval procedure applicable to all balanced linear mixed models.
In this study, we develop procedures for constructing an exact one-sided tolerance interval
and an approximate two-sided tolerance interval for a general setting. The proposed methods
can be applicable to the general balanced mixed models and one-way unbalanced random
models. Our specific interest is given to the unbalanced one-way random model since it is a
very common model used in various practical experiments. The proposed methods are derived
from the concept of generalized pivotal quantities introduced by Weerahandi (1993). In
addition, statistical simulation studies are conducted to verify that the proposed methods can
be recommended for practical use. Partial results of this research have been published in
Technometics, vol 47, pp323-335, 2005.
Subjects
generalized p-values
generalized test variables
generalized confidence intervals
variance components
Publisher
臺北市：國立臺灣大學農藝學系暨研究所
Type
report
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