Interval Estimation for the Bilateral Conformance Proportion under the Linear Regression Model
Date Issued
2012
Date
2012
Author(s)
Lai, Mei-Yu
Abstract
Conformance proportion is commonly used in agriculture management and product evaluation, industrial product quality control or process improvement, environmental monitoring or assessment, pharmaceutical effectiveness evaluation, etc. The bilateral conformance proportion is defined as the probability of a quality characteristic that falls within a specification interval, which can be denoted by , where Y is the quality characteristic of interest and [A,B] is the specification interval. In this study, we focused on constructing confidence limits for the bilateral conformance proportion under the linear regression model. Two construction approaches are proposed. One is based on the concepts of a generalized pivotal quantity, and the other is adopted from the method by Wang and Lam (1996). Detailed simulation studies are conducted to evaluate the performance of these two methods, by comparing their empirical coverage probabilities and expected lengths. The simulation results reveal that the generalized pivotal quantity based method appears to have better coverage probabilities and reasonable expected lengths, which can be suggested in solving generally practical problems. Although the performance of the Wang-Lam method is slightly inferior, it can still be implemented in practical use, due to its computational ease. In addition, some examples are given to illustrate the proposed methods.
Subjects
confidence interval
generalized pivotal quantity
tolerance interval
process capability indices
quality control
Type
thesis
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