A bivariate zero-inflated Poisson control chart: Comments and corrections on earlier results

Abstract

A bivariate zero-inflated Poisson control chart for rare events in an industrial process was presented in the paper of Fatahi et al. (2012). They used a specific copula to address the dependency between the bivariate counts. The copula that they provided did not satisfy the criteria for a copula when the correlation parameter is negative and they did not calculate the upper control limit for the sum of events correctly. We provide proper copula’s and upper control limits and also discuss their choice of parameter estimators. We illustrate our results with simulations.

Keywords:

• Statistical process control
• Zero inflated Poisson distribution
• Copula