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On Nonparametric Multivariate Control Charts Based on Data Depth

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Frontiers in Statistical Quality Control 6

Part of the book series: Frontiers in Statistical Quality Control ((FSQC,volume 6))

Abstract

Most traditional multivariate control charts for monitoring multiple process quality variables are designed and evaluated under the assumption that the process data follow a multivariate normal distribution with known covariance matrix. However, in many practical situations, this assumption of multivariate normality may not hold or may be difficult to verify. Recently, nonparametric Shewhart-type control charts that are based on the notion of simplicial data depth have been proposed for monitoring the locations and scales of multiple process variables. Although these Shewhart charts have potential for addressing the hard problem of multivariate nonparametric quality control, there exist some important unresolved issues with these charts. This paper investigates the effect of the size of the reference sample and the size of the subgroups on the statistical properties of Shewhart-type control charts that are based on simplicial data depth. The sizes of the reference sample and subgroups are the primary factors which determine whether these charts can be designed to achieve sufficiently large in-control average run lengths for

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Author information

Authors and Affiliations

  1. Rutgers, The State University of New Jersey, Newark, NJ, 07102-1895

    Zachary G. Stoumbos

  2. Coral Gables, The University of Miami, FL, 33124-8237

    L. Allison Jones

  3. The University of Alabama, Tuscaloosa, AL, 35487-0226

    William H. Woodall

  4. Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0439

    Marion R. Reynolds Jr.

Authors
  1. Zachary G. Stoumbos
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  2. L. Allison Jones
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  3. William H. Woodall
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  4. Marion R. Reynolds Jr.
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Editor information

Editors and Affiliations

  1. Institut für Statistik und Ökonometrie, Freie Universität Berlin, Garystraße 21, Berlin, 14195, Germany

    Hans-Joachim Lenz  & Peter-Theodor Wilrich  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Stoumbos, Z.G., Jones, L.A., Woodall, W.H., Reynolds, M.R. (2001). On Nonparametric Multivariate Control Charts Based on Data Depth. In: Lenz, HJ., Wilrich, PT. (eds) Frontiers in Statistical Quality Control 6. Frontiers in Statistical Quality Control, vol 6. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57590-7_13

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  • DOI: https://doi.org/10.1007/978-3-642-57590-7_13

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1374-6

  • Online ISBN: 978-3-642-57590-7

  • eBook Packages: Springer Book Archive

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