Control charts for high-quality processes: MAX or CUMAX?

Willem Albers

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    For attribute data with (very) small failure rates control charts were introduced which are based on subsequent groups of r failure times, for some r >= 1. Within this family, it was shown to be attractive to stop once the maximum of such a group is sufficiently small, because this choice allows a very satisfactory nonparametric adaptation. The question we address here is whether a cumulative approach offers even further improvement. Thus instead of fixed groups, we shall use the first sequence of r consecutive sufficiently small failure times to produce a signal. A further reason for considering this type of chart is the fact that it forms the nonparametric counterpart of the well-known sets method.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages14
    Publication statusPublished - Jul 2011

    Publication series

    PublisherDepartment of Applied Mathematics, University of Twente
    ISSN (Print)1874-4850


    • Order statistics
    • Statistical process control
    • Sets method
    • Estimated parameters
    • MSC-62P10
    • Average run length
    • Geometric charts
    • Health care monitoring


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