Introduction of a general class of entropy-based control charts: The Φ-chart
We introduce a new class of Shewhart control charts, namely the f-chart. This new class is based on the cumulative paired f-divergence that generalizes both the cumulative (residual) entropy and the differential entropy. The f-chart contains several subclasses; of which one has a special case, the...
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| Format: | Article |
| Language: | English |
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AGH UNIVERSITY PRESS
2024-12-01
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| Series: | Managerial Economics |
| Online Access: | https://journals.agh.edu.pl/manage/article/view/6556 |
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| author | Benedikt Mangold Jens Konopik |
| author_facet | Benedikt Mangold Jens Konopik |
| author_sort | Benedikt Mangold |
| collection | DOAJ |
| description |
We introduce a new class of Shewhart control charts, namely the f-chart. This new class is based on the cumulative paired f-divergence that generalizes both the cumulative (residual) entropy and the differential entropy. The f-chart contains several subclasses; of which one has 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 f-charts in a showcase scenario, comparing its average run length under the Gaussian and several alternative distributions relevant to process control. 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. The results imply that monitoring a production process using f-charts results in faster detection of out-of-control processes, which can be crucial for a variety of application areas.
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| format | Article |
| id | doaj-art-616ca9cd6adf4298ae8f6b23ac7643f0 |
| institution | DOAJ |
| issn | 1898-1143 2353-3617 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AGH UNIVERSITY PRESS |
| record_format | Article |
| series | Managerial Economics |
| spelling | doaj-art-616ca9cd6adf4298ae8f6b23ac7643f02025-08-20T02:52:09ZengAGH UNIVERSITY PRESSManagerial Economics1898-11432353-36172024-12-0125110.7494/manage.2024.25.1.55Introduction of a general class of entropy-based control charts: The Φ-chartBenedikt Mangold0Jens Konopik1Department of Statistics and Econometrics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, GermanyInstitute of Management, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nuremberg, Germany We introduce a new class of Shewhart control charts, namely the f-chart. This new class is based on the cumulative paired f-divergence that generalizes both the cumulative (residual) entropy and the differential entropy. The f-chart contains several subclasses; of which one has 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 f-charts in a showcase scenario, comparing its average run length under the Gaussian and several alternative distributions relevant to process control. 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. The results imply that monitoring a production process using f-charts results in faster detection of out-of-control processes, which can be crucial for a variety of application areas. https://journals.agh.edu.pl/manage/article/view/6556 |
| spellingShingle | Benedikt Mangold Jens Konopik Introduction of a general class of entropy-based control charts: The Φ-chart Managerial Economics |
| title | Introduction of a general class of entropy-based control charts: The Φ-chart |
| title_full | Introduction of a general class of entropy-based control charts: The Φ-chart |
| title_fullStr | Introduction of a general class of entropy-based control charts: The Φ-chart |
| title_full_unstemmed | Introduction of a general class of entropy-based control charts: The Φ-chart |
| title_short | Introduction of a general class of entropy-based control charts: The Φ-chart |
| title_sort | introduction of a general class of entropy based control charts the φ chart |
| url | https://journals.agh.edu.pl/manage/article/view/6556 |
| work_keys_str_mv | AT benediktmangold introductionofageneralclassofentropybasedcontrolchartsthephchart AT jenskonopik introductionofageneralclassofentropybasedcontrolchartsthephchart |