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A Comparison of Normal Approximation Rules for Attribute Control Charts
Author(s) -
Emura Takeshi,
Lin YiShuan
Publication year - 2015
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1601
Subject(s) - control chart , \bar x and r chart , chart , computer science , binomial (polynomial) , control (management) , statistical process control , binomial distribution , quality (philosophy) , control limits , statistics , data mining , sample (material) , mathematics , artificial intelligence , process (computing) , operating system , philosophy , chemistry , epistemology , chromatography
Control charts, known for more than 80 years, have been important tools for business and industrial manufactures. Among many different types of control charts, the attribute control chart ( np ‐chart or p ‐chart) is one of the most popular methods to monitor the number of observed defects in products, such as semiconductor chips, automobile engines, and loan applications. The attribute control chart requires that the sample size n is sufficiently large and the defect rate p is not too small so that the normal approximation to the binomial works well. Some rules for the required values for n and p are available in the textbooks of quality control and mathematical statistics. However, these rules are considerably different, and hence, it is less clear which rule is most appropriate in practical applications. In this paper, we perform a comparison of five frequently used rules for n and p required for the normal approximation to the binomial. With this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration. Copyright © 2013 John Wiley & Sons, Ltd.