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Properties and performance of the c-chart for attributes data

Author

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  • S. Chakraborti
  • S. W. Human

Abstract

The effects of parameter estimation are examined for the well-known c-chart for attributes data. The exact run length distribution is obtained for Phase II applications, when the true average number of non-conformities, c, is unknown, by conditioning on the observed number of non-conformities in a set of reference data (from Phase I). Expressions for various chart performance characteristics, such as the average run length (ARL), the standard deviation of the run length (SDRL) and the median run length (MDRL) are also obtained. Examples show that the actual performance of the chart, both in terms of the false alarm rate (FAR) and the in-control ARL, can be substantially different from what might be expected when c is known, in that an exceedingly large number of false alarms are observed, unless the number of inspection units (the size of the reference dataset) used to estimate c is very large, much larger than is commonly used or recommended in practice. In addition, the actual FAR and the in-control ARL values can be very different from the nominally expected values such as 0.0027 (or ARL0=370), particularly when c is small, even with large amounts of reference data. A summary and conclusions are offered.

Suggested Citation

  • S. Chakraborti & S. W. Human, 2008. "Properties and performance of the c-chart for attributes data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(1), pages 89-100.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:1:p:89-100
    DOI: 10.1080/02664760701683643
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    Cited by:

    1. Liu, Yafen & He, Zhen & Shu, Lianjie & Wu, Zhang, 2009. "Statistical computation and analyses for attribute events," Computational Statistics & Data Analysis, Elsevier, vol. 53(9), pages 3412-3425, July.
    2. Yadpirun Supharakonsakun, 2024. "Bayesian Control Chart for Number of Defects in Production Quality Control," Mathematics, MDPI, vol. 12(12), pages 1-10, June.
    3. Johannssen, Arne & Chukhrova, Nataliya & Castagliola, Philippe, 2022. "The performance of the hypergeometric np chart with estimated parameter," European Journal of Operational Research, Elsevier, vol. 296(3), pages 873-899.

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