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

Author

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  • Edwin R. van den Heuvel
  • Stephan A. W. van Driel
  • Zhuozhao Zhan

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.

Suggested Citation

  • Edwin R. van den Heuvel & Stephan A. W. van Driel & Zhuozhao Zhan, 2022. "A bivariate zero-inflated Poisson control chart: Comments and corrections on earlier results," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(10), pages 3438-3445, May.
    • Handle: RePEc:taf:lstaxx:v:51:y:2022:i:10:p:3438-3445
    DOI: 10.1080/03610926.2020.1736304
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    Cited by:

    1. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-52, November.
    2. Dimuthu Fernando & Mohammed Alqawba & Manar Samad & Norou Diawara, 2022. "Review of Copula for Bivariate Distributions of Zero-Inflated Count Time Series Data," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 11(6), pages 1-28, November.

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