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A generalized statistical control chart for over‐ or under‐dispersed data
Author(s) -
Sellers Kimberly F.
Publication year - 2012
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1215
Subject(s) - poisson distribution , negative binomial distribution , count data , poisson binomial distribution , zero inflated model , compound poisson distribution , mathematics , control chart , binomial distribution , bernoulli's principle , geometric distribution , quasi likelihood , statistics , chart , dispersion (optics) , index of dispersion , beta binomial distribution , computer science , probability distribution , poisson regression , physics , population , demography , process (computing) , sociology , optics , thermodynamics , operating system
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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