MINDCUMIN charts

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

    Research output: Book/ReportReportProfessional

    12 Downloads (Pure)

    Abstract

    A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages15
    Publication statusPublished - Sep 2007

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.LNCS4549/1851
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • METIS-241941
    • MSC-62G30
    • MSC-62P30
    • MSC-62L10
    • EWI-11131
    • Order statistics
    • Statistical Process Control
    • Phase II control limits
    • CUSUM-chart
    • IR-64373

    Cite this

    Albers, WW., & Kallenberg, W. C. M. (2007). MINDCUMIN charts. Enschede: University of Twente, Department of Applied Mathematics.
    Albers, Willem/Wim ; Kallenberg, W.C.M. / MINDCUMIN charts. Enschede : University of Twente, Department of Applied Mathematics, 2007. 15 p.
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    abstract = "A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.",
    keywords = "METIS-241941, MSC-62G30, MSC-62P30, MSC-62L10, EWI-11131, Order statistics, Statistical Process Control, Phase II control limits, CUSUM-chart, IR-64373",
    author = "Willem/Wim Albers and W.C.M. Kallenberg",
    note = "eemcs-eprint-11131",
    year = "2007",
    month = "9",
    language = "Undefined",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "LNCS4549/1851",

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    Albers, WW & Kallenberg, WCM 2007, MINDCUMIN charts. University of Twente, Department of Applied Mathematics, Enschede.

    MINDCUMIN charts. / Albers, Willem/Wim; Kallenberg, W.C.M.

    Enschede : University of Twente, Department of Applied Mathematics, 2007. 15 p.

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - MINDCUMIN charts

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    N1 - eemcs-eprint-11131

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    N2 - A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.

    AB - A serious drawback of classical control charts is their high sensitivity to deviations from normality. By now, many alternative procedures, often of a nonparametric nature, have been proposed. A danger with these competitors is that unrealistically large Phase I samples might be needed. This can be avoided by using groups of, rather than individual (IND), observations during Phase II. A recently introduced successful example is the CUMIN chart: a signal occurs as soon as m consecutive observations all exceed some suitably chosen upper limit. An interesting question is how m should be chosen in this cumulative minimum. If large (small shifts are likely to occur, m should be small (large). As often the magnitude of possible shifts is unclear, it is attractive to be flexible w.r.t. the choice of m. In the present paper a procedure is developed which achieves this goal by combining an IND and a CUMIN procedure. As input minima of small blocks (e.g. pairs or triples) of observations should be used, to avoid recurrence of the problem of the need for unrealistically large Phase I samples.

    KW - METIS-241941

    KW - MSC-62G30

    KW - MSC-62P30

    KW - MSC-62L10

    KW - EWI-11131

    KW - Order statistics

    KW - Statistical Process Control

    KW - Phase II control limits

    KW - CUSUM-chart

    KW - IR-64373

    M3 - Report

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    PB - University of Twente, Department of Applied Mathematics

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    ER -

    Albers WW, Kallenberg WCM. MINDCUMIN charts. Enschede: University of Twente, Department of Applied Mathematics, 2007. 15 p.