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

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.

[1]  Sharad Borle,et al.  Computing with the COM-Poisson distribution , 2003 .

[2]  Aamir Saghir,et al.  The Use of Probability Limits of COM–Poisson Charts and their Applications , 2013, Qual. Reliab. Eng. Int..

[3]  Nan Chen,et al.  Attribute control charts using generalized zero‐inflated Poisson distribution , 2008, Qual. Reliab. Eng. Int..

[4]  Seth D Guikema,et al.  A Flexible Count Data Regression Model for Risk Analysis , 2008, Risk analysis : an official publication of the Society for Risk Analysis.

[5]  Richard S. Leavenworth,et al.  The Negative Binomial Model for Counts in Units of Varying Size , 1976 .

[6]  Willem Wim Albers.  Control charts for health care monitoring under overdispersion , 2009 .

[7]  P. Consul,et al.  A Generalization of the Poisson Distribution , 1973 .

[8]  M. A. Mohammed,et al.  Overdispersion in health care performance data: Laney’s approach , 2006, Quality and Safety in Health Care.

[9]  Galit Shmueli,et al.  Conjugate Analysis of the Conway-Maxwell-Poisson Distribution , 2006 .

[10]  Felix Famoye,et al.  Statistical control charts for shifted generalized poisson distribution , 1994 .

[11]  Fred Spiring,et al.  Introduction to Statistical Quality Control , 2007, Technometrics.

[12]  James C. Benneyan,et al.  Statistical Control Charts Based on a Geometric Distribution , 1992 .

[13]  T. Minka,et al.  A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution , 2005 .

[14]  D J Spiegelhalter,et al.  Handling over-dispersion of performance indicators , 2005, Quality and Safety in Health Care.