Negative binomial charts for monitoring high-quality processes

Willem Albers

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    Abstract

    Good control charts for high quality processes are often based on the number of successes between failures. Geometric charts are simplest in this respect, but slow in recognizing moderately increased failure rates p. Improvement can be achieved by waiting until r > 1 failures have occurred, i.e. by using negative binomial charts.In this paper we analyze such charts in some detail. On the basis of a fair comparison, we demonstrate how the optimal r is related to the degree of increase of p. As in practice p will usually be unknown, we also analyze the estimated version of the charts. In particular, simple corrections are derived to control the non-negligible effects of this estimation step.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Faculty of Mathematical Sciences
    Number of pages17
    Publication statusPublished - Sep 2008

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1881
    ISSN (Print)1874-4850

    Keywords

    • MSC-62P10
    • MSC-62F12
    • MSC-62C05

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