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A general class of entropy based control charts

Author

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  • Mangold, Benedikt
  • Konopik, Jens

Abstract

We introduce a new class of Shewhart control charts, namely the phi-chart. This new class is based on the cumulative paired phi-divergence that generalizes both the cumulative (residual) entropy and the differential entropy. The phi-chart contains several subclasses; of which one has as a special case the G-chart, which uses Gini's mean difference as a measure of dispersion. We investigate the performance of three of the subclasses of phi-charts in a showcase scenario, comparing its average run length under the Gaussian and several alternative distributions. We find especially the new Leik control chart to outperform classical Shewhart charts, which are based on ranks, standard deviation, or Gini's mean difference. Monitoring a production process using phi-charts implies a faster detection of an out-of-control process, which can be crucial for a variety of application areas.

Suggested Citation

  • Mangold, Benedikt & Konopik, Jens, 2017. "A general class of entropy based control charts," FAU Discussion Papers in Economics 04/2017, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    • Handle: RePEc:zbw:iwqwdp:042017
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