Browsing by Author "Tsung, Fugee"

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Constructing Tolerance Intervals for the Number of Defectives Using Both High-and Low-Resolution Data
(2017-10-01)
Wang, Hsiuying
;
Tsung, Fugee
;
統計學研究所
;
Institute of Statistics
Defect inspection is important in many industries, such as in the manufacturing and pharmaceutical industries. Existing methods usually use either low-resolution data, which are obtained from less precise measurements, or high-resolution data, which are obtained from more precise measurements, to estimate the number of defectives in a given amount of goods produced. In this study, a novel approach is proposed that combines the two types of data to construct tolerance intervals with a desired average coverage probability. A simulation study shows that the derived tolerance intervals can lead to better performance than a tolerance interval that is constructed based on only the low-resolution data. In addition, a real-data example shows that the tolerance interval based on only the low-resolution data is more conservative than the tolerance intervals based on both high-resolution and low-resolution data.
Tolerance Intervals With Improved Coverage Probabilities for Binomial and Poisson Variables
(2009-02-01)
Wang, Hsiuying
;
Tsung, Fugee
;
統計學研究所
;
Institute of Statistics
The construction of tolerance intervals (TIs) for discrete variables, such as binomial and Poisson variables, has been critical in industrial applications in various sectors, including manufacturing and pharmaceuticals. Inaccurate estimation of coverage probabilities leads to improper construction of tolerance intervals and may lead to serious financial losses for the manufacturers. This article proposes procedures to compute the exact minimum and average coverage probabilities of the tolerance intervals for Poisson and binomial variables. These procedures are illustrated with examples and real data applications. Based on these procedures, improved tolerance intervals are proposed that can ensure that the true minimum or average coverage probabilities are very close to the nominal levels.