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Control Charts for Monitoring Correlated Poisson Counts with an Excessive Number of Zeros
Author(s) -
Rakitzis Athanasios C.,
Weiß Christian H.,
Castagliola Philippe
Publication year - 2017
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2017
Subject(s) - count data , poisson distribution , autocorrelation , control chart , zero inflated model , statistics , overdispersion , mathematics , zero (linguistics) , independence (probability theory) , inflation (cosmology) , poisson regression , statistical process control , series (stratigraphy) , process (computing) , computer science , paleontology , sociology , theoretical physics , population , linguistics , philosophy , demography , physics , biology , operating system
The zero‐inflated Poisson distribution serves as an appropriate model when there is an excessive number of zeros in the data. This phenomenon frequently occurs in count data from high‐quality processes. Usually, it is assumed that these counts exhibit serial independence, while a more realistic assumption is the existence of an autocorrelation structure between them. In this work, we study control charts for monitoring correlated Poisson counts with an excessive number of zeros. Zero‐inflation in the process is captured via appropriate integer‐valued time series models. Extensive numerical results are provided regarding the performance of the considered charts in the detection of changes in the mean of the process as well as the effects of zero‐inflation on them. Finally, a real‐data practical application is given. Copyright © 2016 John Wiley & Sons, Ltd.