On Control Charts Based on the Generalized Poisson Model

Abstract

The Poisson distribution is widely used to fit count data such as the number of nonconformities in a product unit. However, this distribution fails to fit the defect data in a high-quality manufacturing environment when over-dispersion occurs. In this paper, the generalized Poisson distribution is studied as an alternative distribution. The generalized Poisson distribution is flexible and capable of dealing with over-dispersed data. In particular, the interpretation of parameters is discussed and statistical monitoring procedures for count data that can be modeled by the generalized Poisson distribution are studied. Based on the generalized Poisson distribution, two different procedures are discussed for an effective process monitoring. Sensitivity analyses of the two monitoring procedures are also presented. To validate the use of the generalized Poisson distribution, three statistical tests for testing the Poisson distribution against the generalized Poisson alternative are also investigated and compared.