On Designing a New Control Chart Using the Generalized Conway–Maxwell–Poisson Distribution to Monitor Count Data

Many researchers employed Poisson distribution-based control charts to monitor count data. Nevertheless, these charts can handle count data that deviate from the Poisson assumption of equal mean and variance. This paper suggests a new control chart (CC) that uses the generalized Conway–Maxwell–Poiss...

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Bibliographic Details
Published in:Processes 2024-04, Vol.12 (4), p.688
Main Authors: Mustafa, Fakhar, Sherwani, Rehan Ahmad Khan, Raza, Muhammad Ali, Darwish, Jumanah Ahmed
Format: Article
Language:English
Subjects:
Canada
Control charts
Control limits
El Salvador
Expected values
Inflation (Finance)
Pakistan
Performance evaluation
Poisson distribution
Probability
Process controls
Random variables
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Summary:Many researchers employed Poisson distribution-based control charts to monitor count data. Nevertheless, these charts can handle count data that deviate from the Poisson assumption of equal mean and variance. This paper suggests a new control chart (CC) that uses the generalized Conway–Maxwell–Poisson (GCOMP) distribution, which can deal with count data that have different levels of dispersion and zero-inflation (ZI). The proposed chart is designed considering the total number of counts. The main advantage of this study is that it pays attention to the tails of the count data when monitoring the process. The performance is measured by the average run length using L control limits at different sample sizes and parametric settings. The findings demonstrate that, for count data with varying tail behaviors, the proposed chart performs better compared to existing CCs. ZI count data can also be monitored with the proposed chart. The proposed chart can be applied in a variety of fields, as verified by the examples provided in this paper.
ISSN:2227-9717
2227-9717
DOI:10.3390/pr12040688