Exceedance probabilities for parametric control charts

Willem Albers, Wilbert C.M. Kallenberg, Sri Nurdiati

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    Abstract

    Common control charts assume normality and known parameters. Quite often these assumptions are not valid and large relative errors result in the usual performance characteristics, such as the false alarm rate or the average run length. A fully nonparametric approach can form an attractive alternative but requires more Phase I observations than are usually available. Sufficiently large parametric families then provide realistic intermediate models. In this paper the performance of charts based on such families is considered. Exceedance probabilities of the resulting stochastic performance characteristics during in-control are studied. Corrections are derived to ensure that such probabilities stay within prescribed bounds. Attention is also devoted to the impact of the corrections for an out-of-control process. Simulations are presented both for illustration and to demonstrate that the approximations obtained are sufficiently accurate for use in practice.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages16
    Publication statusPublished - 2002

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    No.1650
    ISSN (Print)0169-2690

    Keywords

    • MSC-62G15
    • MSC-62P30

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