Empirical nonparametric control charts: estimation effects and corrections

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

    Research output: Book/ReportReportProfessional

    55 Downloads (Pure)

    Abstract

    Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages17
    Publication statusPublished - 2002

    Publication series

    NameMemorandum Faculty of Mathematical Sciences
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1651
    ISSN (Print)0169-2690

    Keywords

    • MSC-62G15
    • MSC-62P30
    • IR-65837
    • METIS-206704
    • EWI-3471

    Cite this

    Albers, WW., & Kallenberg, W. C. M. (2002). Empirical nonparametric control charts: estimation effects and corrections. (Memorandum Faculty of Mathematical Sciences; No. 1651). Enschede: University of Twente, Department of Applied Mathematics.
    Albers, Willem/Wim ; Kallenberg, W.C.M. / Empirical nonparametric control charts: estimation effects and corrections. Enschede : University of Twente, Department of Applied Mathematics, 2002. 17 p. (Memorandum Faculty of Mathematical Sciences; 1651).
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    abstract = "Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.",
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    author = "Willem/Wim Albers and W.C.M. Kallenberg",
    note = "Imported from MEMORANDA",
    year = "2002",
    language = "Undefined",
    series = "Memorandum Faculty of Mathematical Sciences",
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    Albers, WW & Kallenberg, WCM 2002, Empirical nonparametric control charts: estimation effects and corrections. Memorandum Faculty of Mathematical Sciences, no. 1651, University of Twente, Department of Applied Mathematics, Enschede.

    Empirical nonparametric control charts: estimation effects and corrections. / Albers, Willem/Wim; Kallenberg, W.C.M.

    Enschede : University of Twente, Department of Applied Mathematics, 2002. 17 p. (Memorandum Faculty of Mathematical Sciences; No. 1651).

    Research output: Book/ReportReportProfessional

    TY - BOOK

    T1 - Empirical nonparametric control charts: estimation effects and corrections

    AU - Albers, Willem/Wim

    AU - Kallenberg, W.C.M.

    N1 - Imported from MEMORANDA

    PY - 2002

    Y1 - 2002

    N2 - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.

    AB - Due to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and nonnormality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a larger model is inadequate and nothing remains but to consider nonparametric charts. In principle these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage which seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyze under what conditions nonparametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes which are markedly less huge (but still larger than the customary range). These corrections serve to control the behavior during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection clearly will be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.

    KW - MSC-62G15

    KW - MSC-62P30

    KW - IR-65837

    KW - METIS-206704

    KW - EWI-3471

    M3 - Report

    T3 - Memorandum Faculty of Mathematical Sciences

    BT - Empirical nonparametric control charts: estimation effects and corrections

    PB - University of Twente, Department of Applied Mathematics

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    Albers WW, Kallenberg WCM. Empirical nonparametric control charts: estimation effects and corrections. Enschede: University of Twente, Department of Applied Mathematics, 2002. 17 p. (Memorandum Faculty of Mathematical Sciences; 1651).