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A generalized statistical control chart for over- or under-dispersed data

Authors

  • Kimberly F. Sellers

    Corresponding author
    1. Department of Mathematics and Statistics, Georgetown University, Washington, DC, U.S.A.
    • Department of Mathematics and Statistics, Georgetown University, Washington, DC, U.S.A.
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Abstract

The Poisson distribution is a popular distribution used to describe count information, from which control charts involving count data have been established. Several works recognize the need for a generalized control chart to allow for data over-dispersion; however, analogous arguments can also be made to account for potential under-dispersion. The Conway–Maxwell–Poisson (COM-Poisson) distribution is a general count distribution that relaxes the equi-dispersion assumption of the Poisson distribution, and in fact encompasses the special cases of the Poisson, geometric, and Bernoulli distributions. Accordingly, a flexible control chart is developed that encompasses the classical Shewart charts based on the Poisson, Bernoulli (or binomial), and geometric (or negative binomial) distributions. Copyright © 2011 John Wiley & Sons, Ltd.

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