Conformance Proportions in a Normal Variance Components Model
Date Issued
2012
Date
2012
Author(s)
Lee, Hsin-I
Abstract
Conformance proportion is defined as the proportion of a performance characteristic of interest that falls within a prespecified acceptance region. It can be used not only in manufacture industry but also in agricultural management or environmental monitoring. For instance, determining best harvest timing for forage maize under an appropriate range of dry matter content, monitoring the sweetness of fruits to
be above a lower limit, or requiring the concentration of a toxin to be below an upper limit in pesticide residue tests. It is of desire to estimate the probability that
a random variable exceeds a specification limit or falls into a specification region, which is essentially the conformance proportion.
In this dissertation, we propose the approach of a conformance proportion as an alternative to that of a tolerance interval for practical use. First, we discuss
the connections between the two approaches. Then, two methods are developed for computing confidence limits for bilateral conformance proportions, one is based on the concept of a generalized pivotal quantity and the other is based on the modified large sample method. For unilateral conformance proportions, we also propose two methods for interval estimation, the first one is also based on the concept of a generalized pivotal quantity and the second one is based on the Student’s t distribution. A bootstrap calibration approach is adapted for both bilateral and unilateral conformance proportions to have empirical coverage probability sufficiently close to the nominal level. Furthermore, we consider the situations with unbalanced data scenarios. Some examples are given to illustrate the proposed methods. The performances of these approaches are evaluated by detailed statistical simulation studies, showing that they can be recommended for practical use.
Subjects
Tolerance interval
Generalized pivotal quantity
Modified large sample
Parametric bootstrap method
SDGs
Type
thesis
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