Empirical nonparametric control charts: estimation effects and corrections

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

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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.
    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.