Construction of Tolerance Intervals Using the Concept of Generalized Pivotal Quantity
Date Issued
2005
Date
2005
Author(s)
Lin, Tsai-Yu
DOI
en-US
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 dissertation, we develop procedures for one- and two-sided $ eta$-content and $ eta$-expectation tolerance intervals for normal general linear models in which there exists a set of independent scaled chi-squared random variables. The developed procedures are based on the concept of generalized pivotal quantities, which has been frequently used to obtain confidence intervals in ituations where standard procedures do not lead to useful solutions.
We first derive the tolerance intervals for a general setting. Then we implement the derived procedures in the general balanced mixed linear models, the unbalanced one-way random models, and the unbalanced one-way random models with covariates under heterogeneous error variances. For the one-sided case, it does not involve any approximations, resulting in an exact method. For the two-sided case, it is good approximate. It is shown that the use of generalized pivotal quantities 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.
Subjects
廣義 p 值
線性模型
卡方近似
變異數成份
廣義信賴區間
Chi-squared approximation
Generalized p-value
Generalized confidence interval
Linear model
Variance component
Type
thesis
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