Behavior of EWMA type control charts for small smoothing parameters |
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| Affiliation: | 1. Department of Statistics, European University Viadrina, PO Box 1786, 15207 Frankfurt (Oder), Germany;2. Department of Statistics, University of Augsburg, D-86159 Augsburg, Germany;1. Department of Pediatrics and Adolescent Medicine, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany;2. Department of Medicine 1, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany;3. iThera Medical GmbH, München, Germany;4. Ludwig Demling Center of Excellence, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nürnberg, Germany;5. Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universität Erlangen-Nürnberg, Nürnberg, Germany;6. Institute of Medical Biotechnology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Nürnberg, Germany;7. Institute for Biological and Medical Imaging, Helmholtz Zentrum München, München, Germany;8. Chair for Biological Imaging, TranslaTUM, Technische Universität München, München, Germany;1. Department of Otolaryngology, Head and Neck Surgery, University of Ulm, Prittwitzstr. 43, 89075 Ulm, Germany;2. Department of Otolaryngology, Head and Neck Surgery, Technical University of Munich, Ismaninger Str. 22, 81675 Munich, Germany;3. Molecular Pathology South Bavaria, Trogerstraße 18, 81675 Munich, Germany;4. Division of Neuropathology, Institute of Pathology, Technical University of Munich, Ismaninger Str. 22, 81675 Munich, Germany;5. Institute for Medical Statistics and Epidemiology, Technical University of Munich, Ismaninger Str. 22, 81675 Munich, Germany;6. Department of Gynecology and Obstetrics, University of Regensburg, Landshuter Str. 65, 93053 Regensburg, Germany;1. Zentrum für elektronische Korrelation und Magnetismus, Universität Augsburg, Universitätsstr. 1, 86159 Augsburg, Germany;2. Technische Universität München, Physik-Department E21, James-Franck-Str. 1, 85748 Garching, Germany;3. Max-Planck-Institut für Festkörperforschung, Heisenbergstr. 1, 70569 Stuttgart, Germany;1. Institut für Physik, Universität Augsburg, Augsburg, Germany;2. Deutsches Fernerkundungsdatenzentrum, Deutsches Zentrum für Luft- und Raumfahrt, Weßling-Oberpfaffenhofen, Germany;3. Institut für Astro- und Teilchenphysik, Universität Innsbruck, Innsbruck, Austria;4. Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany;5. Instituto de Astronomía, Universidad Católica del Norte, Antofagasta, Chile;1. Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;2. VU University Amsterdam, The Netherlands;3. Uppsala Universitet, Department of Mathematics, P.O. Box 480, 751 06 Uppsala, Sweden;4. Mathematisch Instituut, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands |
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| Abstract: | A general family of EWMA charts is considered for monitoring an arbitrary parameter of the target process. The distribution of the run length is analysed for the case when the smoothing parameter tends to zero. The key impact on the results from the use of the exact variance of the control statistics vs. the asymptotic one and the presence of a head start. For fixed head start, the run lengths for both the exact and asymptotic monitoring procedures degenerate to a binary quantity. To guarantee a feasible monitoring procedure, the head start has to be chosen proportional to the smoothing parameter and the control statistics have to be modified when used with the asymptotic variance. This result underlines the weakness of schemes with a fixed head start and of schemes based on the asymptotic variance if the smoothing parameter is small. The assumptions on the target process are very weak, and are usually satisfied for stationary processes. In addition, the asymptotic equivalence of the EWMA schemes and of repeated significance tests is shown. |
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| Keywords: | EWMA chart Stationary process Statistical process control Run length |
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