Zero-inflated poisson model in statistical process control

Abstract

Poisson distribution has often been used for count related data. However, this model does not provide a good fit to actual data when there is a frequent or excessive number of zero counts. For example, in a near zero-defect manufacturing environment, there are many zero-defect counts even for fairly large sample size. In such a situation, the zero-inflated Poisson distribution is more appropriate. In this paper, the use of this distribution is investigated. In particular, various tests of Poisson distribution and zero-inflated Poisson alternative are compared. When the model is used in statistical process control, control limits can then be derived based on the zero-inflated Poisson model when the Poisson distribution is rejected in favour of the zero-inflated Poisson alternative. Furthermore, sensitivity analysis of such a control chart is also presented. © 2001 Published by Elsevier Science B.V.