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

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.

Automated summary

In this paper, a bivariate zero-inflated Poisson control chart is proposed for rare events in an industrial process. The authors address the dependency between the bivariate counts using a specific copula. However, they find that the copula provided does not meet the criteria in cases where the correlation parameter is negative, and the upper control limit for the sum of events is not calculated correctly. This study presents proper copulas and upper control limits, and discusses the choice of parameter estimators. The results are illustrated using simulations.