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The Use of Probability Limits of COM–Poisson Charts and their Applications

Authors


Correspondence to: Aamir Saghir, Department of Mathematics, Institute of Statistics, Zhejiang University Yuquan, Campus, P.R. China

E-mail: aamirstat@yahoo.com

Abstract

The conventional c and u charts are based on the Poisson distribution assumption for the monitoring of count data. In practice, this assumption is not often satisfied, which requires a generalized control chart to monitor both over-dispersed as well as under-dispersed count data. 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. In this study, the exact k-sigma limits and true probability limits for COM–Poisson distribution chart have been proposed. The comparison between the 3-sigma limits, the exact k-sigma limits, and the true probability limits has been investigated, and it was found that the probability limits are more efficient than the 3-sigma and the k-sigma limits in terms of (i) low probability of false alarm, (ii) existence of lower control limits, and (iii) high discriminatory power of detecting a shift in the parameter (particularly downward shift). Finally, a real data set has been presented to illustrate the application of the probability limits in practice. Copyright © 2012 John Wiley & Sons, Ltd.

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