Improved data driven control charts

Willem/Wim Albers, W.C.M. Kallenberg

    Research output: Book/ReportReportProfessional

    18 Downloads (Pure)

    Abstract

    Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages10
    Publication statusPublished - 2006

    Publication series

    NameApplied Mathematics Memoranda
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1791
    ISSN (Print)0169-2690

    Keywords

    • IR-65596
    • EWI-2690
    • MSC-62G32
    • MSC-62G30
    • MSC-62P30
    • METIS-230991

    Cite this

    Albers, WW., & Kallenberg, W. C. M. (2006). Improved data driven control charts. (Applied Mathematics Memoranda; No. 1791). Enschede: University of Twente, Department of Applied Mathematics.
    Albers, Willem/Wim ; Kallenberg, W.C.M. / Improved data driven control charts. Enschede : University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; 1791).
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    author = "Willem/Wim Albers and W.C.M. Kallenberg",
    year = "2006",
    language = "Undefined",
    series = "Applied Mathematics Memoranda",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "1791",

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    Albers, WW & Kallenberg, WCM 2006, Improved data driven control charts. Applied Mathematics Memoranda, no. 1791, University of Twente, Department of Applied Mathematics, Enschede.

    Improved data driven control charts. / Albers, Willem/Wim; Kallenberg, W.C.M.

    Enschede : University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; No. 1791).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Improved data driven control charts

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    PY - 2006

    Y1 - 2006

    N2 - Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.

    AB - Classical control charts for monitoring the mean are based on the assumption of normality. When normality fails, these control charts are no longer valid and serious errors often arise. Data driven control charts, which choose between the normal chart, a parametric one and a nonparametric chart, have recently been proposed to solve the problem. They also correct for estimation errors due to estimation of the parameters involved or, in the nonparametric chart, for estimation of the appropriate quantiles of the distribution. In many cases these data driven control charts are performing very well. However, when the data point towards the nonparametric chart no satisfactory solution is obtained unless the number of Phase I observations is very large. The problem is that accurate estimation of an extreme quantile in a nonparametric way needs a huge number of observations. Replacing the nonparametric individual chart by a nonparametric chart for grouped observations does the job. These improved data driven control charts are presented here. Ready-made formulas are given, which make implementation of the charts quite straightforward. An application on real data clearly shows the improvement: estimation of extreme quantiles is replaced by estimation of ordinary quantiles, which can be done in an accurate way for common sample sizes.

    KW - IR-65596

    KW - EWI-2690

    KW - MSC-62G32

    KW - MSC-62G30

    KW - MSC-62P30

    KW - METIS-230991

    M3 - Report

    T3 - Applied Mathematics Memoranda

    BT - Improved data driven control charts

    PB - University of Twente, Department of Applied Mathematics

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    ER -

    Albers WW, Kallenberg WCM. Improved data driven control charts. Enschede: University of Twente, Department of Applied Mathematics, 2006. 10 p. (Applied Mathematics Memoranda; 1791).