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Run and Scan Rules in Statistical Process Monitoring

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Handbook of Scan Statistics

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Abstract

In this paper, we provide an overview of the use of run and scan rules in statistical process monitoring. Although we focus on control charts, supplemented with various stop** rules based on run and scan statistics, several other monitoring procedures that incorporate run and scan statistics are reviewed as well. Rules based on the notion of scans have been incorporated in the traditional Shewhart charts in order to improve their performance and at the same time preserve their simplicity. In our presentation we review the major types of run and scan rules currently available in the literature of control charts and highlight how they are implemented in practice. A unified framework for studying the characteristics of run- and scan-based control charts by exploiting a Markov chain approach is also provided. We end up with some concluding remarks and some directions for future research in the area under review.

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Acknowledgements

The authors would like to thank the anonymous reviewer for the useful suggestions and comments made, which helped us to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

    Sotiris Bersimis & Markos V. Koutras

  2. Department of Statistics and Actuarial-Financial Mathematics, University of Aegean, Karlovasi, Samos, Greece

    Athanasios C. Rakitzis

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  1. Sotiris Bersimis
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  2. Markos V. Koutras
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  3. Athanasios C. Rakitzis
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Corresponding author

Correspondence to Markos V. Koutras .

Editor information

Editors and Affiliations

  1. University of Connecticut Dept. Statistics, Storrs, CT, USA

    Joseph Glaz

  2. University of Pireaus Dept. Statistics & Insurance Sciences, Piraeus, Greece

    Markos V. Koutras

Section Editor information

  1. Department of Statistics, University of Connecticut, Storrs, CT, USA

    Joseph Glaz

  2. Department of Statistics and Insurance Science, University of Piraeus, Piraeus, Greece

    Markos V. Koutras

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Bersimis, S., Koutras, M.V., Rakitzis, A.C. (2020). Run and Scan Rules in Statistical Process Monitoring. In: Glaz, J., Koutras, M. (eds) Handbook of Scan Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8414-1_55-1

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