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A comparison of normal approximation rules for attribute control charts

Author

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  • Emura, Takeshi
  • Lin, Yi-Shuan

Abstract

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. Based on this result, we also refine the existing rules to develop a new rule that has a reliable performance. Datasets are analyzed for illustration.

Suggested Citation

  • Emura, Takeshi & Lin, Yi-Shuan, 2013. "A comparison of normal approximation rules for attribute control charts," MPRA Paper 51029, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:51029
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    File URL: https://mpra.ub.uni-muenchen.de/51029/1/MPRA_paper_51029.pdf
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    References listed on IDEAS

    as
    1. Zeileis, Achim & Hornik, Kurt & Murrell, Paul, 2009. "Escaping RGBland: Selecting colors for statistical graphics," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3259-3270, July.
    2. Wang, Hsiuying, 2009. "Comparison of p control charts for low defective rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4210-4220, October.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Long, Ting-Hsuan & Emura, Takeshi, 2014. "A control chart using copula-based Markov chain models," MPRA Paper 57419, University Library of Munich, Germany.

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    More about this item

    Keywords

    attribute control chart; binomial distribution; np-chart; p-chart; statistical process control;
    All these keywords.

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • L6 - Industrial Organization - - Industry Studies: Manufacturing

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