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Control limits for p control charts with small subgroup sizes.

Marilyn K Hart1, Robert F Hart, Stephen Schmaltz

  • 1From the College of Business Administration, The University of Wisconsin Oshkosh, Oshkosh, WI 54901, USA. hart@uwosh.edu

Quality Management in Health Care
|April 12, 2007
PubMed
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The p chart, used in many industries, often relies on 3sigma limits. This study suggests using the exact binomial distribution for more accurate monitoring, especially with small subgroups.

Area of Science:

  • Quality Control
  • Statistical Process Control
  • Healthcare Analytics

Background:

  • The p chart is a standard tool for monitoring proportions in various sectors, including manufacturing and healthcare.
  • Conventional methods use 3sigma limits based on the normal approximation to the binomial distribution.
  • This approach can be problematic, especially with small subgroup sizes.

Purpose of the Study:

  • To review and propose an alternative to the conventional 3sigma limits for p charts.
  • To address the limitations of the normal approximation in p chart analysis.
  • To improve the accuracy of process monitoring, particularly for small subgroups.

Main Methods:

  • Review of existing p chart methodologies.
  • Application of the exact binomial distribution for calculating control limits.

Related Experiment Videos

  • Comparison of exact binomial limits with traditional 3sigma limits.
  • Analysis of data with small subgroups.

    • Main Results:

    • The normal approximation to the binomial distribution can lead to inaccuracies with small subgroups.
    • The use of exact binomial probability control limits offers a more appropriate method.
    • Modified control limits derived from the exact binomial distribution effectively address issues with small subgroups.
    • An example demonstrated the successful application with only 4 small subgroups.

    Conclusions:

    • The conventional 3sigma limits for p charts are not always appropriate, especially with small subgroups.
    • Employing the exact binomial distribution provides a more robust and accurate method for statistical process control.
    • Probability control limits and modified control limits based on the exact binomial distribution resolve problems associated with small sample sizes in p charts.