A bivariate zero-inflated Poisson control chart: Comments and corrections on earlier results. Issue 10 (19th May 2022)

• Record Type: Journal Article
• Authors: van den Heuvel, Edwin R.; van Driel, Stephan A. W.; Zhan, Zhuozhao
• Is Part Of: Communications in statistics. Volume 51:Issue 10(2022)
• Page Start: 3438
• Page End: 3445
• Publication Date: 2022-05-19
• Subjects: Statistical process control -- Zero inflated Poisson distribution -- Copula; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2020.1736304
• Languages: English
• ISSNs: 0361-0926

Abstract

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.