Statistical process control of overdispersed count data based on one-parameter Poisson mixture models

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dc.contributor.authorJesus, Bruno D.
dc.contributor.authorFerreira, Paulo H.
dc.contributor.authorBoaventura, Laion L.
dc.contributor.authorFiaccone, Rosemeire L.
dc.contributor.authorBertoli, Wesley
dc.contributor.authorRamos, Pedro L.
dc.contributor.authorLouzada, Francisco
dc.date.accessioned2025-01-20T22:00:23Z
dc.date.available2025-01-20T22:00:23Z
dc.date.issued2022
dc.description.abstractThe Poisson distribution is a discrete model widely used to analyze count data. Statistical control charts based on this distribution, such as the c$c$ and u$u$ charts, are relatively well-established in the literature. Nevertheless, many studies suggest the need for alternative approaches that allow for modeling overdispersion, a phenomenon that can be observed in several fields, including biology, ecology, healthcare, marketing, economics, and industry. The one-parameter Poisson mixture distributions, whose literature is extensive and essential, can model extra-Poisson variability, accommodating different overdispersion levels. The distributions belonging to this class of models, including the Poisson-Lindley (PL), Poisson-Shanker (PSh), and Poisson-Sujatha (PSu) models, can thus be used as interesting alternatives to the usual Poisson and COM-Poisson distributions for analyzing count data in several areas. In this paper, we consider the class of probabilistic models mentioned above (as well as the cited three members of such a class) to develop novel and useful statistical control charts for counting processes, monitoring count data that exhibit overdispersion. The performance of the so-called one-parameter Poisson mixture charts, namely the PLc$\text{PL}_c$-PLu$\text{PL}_u$, PShc$\text{PSh}_c$-PShu$\text{PSh}_u$, and PSuc$\text{PSu}_c$-PSuu$\text{PSu}_u$ charts, is measured by the average run length in exhaustive numerical simulations. Some data sets are used to illustrate the applicability of the proposed methodology.
dc.fuente.origenWOS
dc.identifier.doi10.1002/qre.3077
dc.identifier.eissn1099-1638
dc.identifier.issn0748-8017
dc.identifier.urihttps://doi.org/10.1002/qre.3077
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/93721
dc.identifier.wosidWOS:000752450800001
dc.issue.numero5
dc.language.isoen
dc.pagina.final2344
dc.pagina.inicio2324
dc.revistaQuality and reliability engineering international
dc.rightsacceso restringido
dc.subjectaverage run length
dc.subjectcount data
dc.subjectone-parameter poisson mixture charts
dc.subjectoverdispersion
dc.titleStatistical process control of overdispersed count data based on one-parameter Poisson mixture models
dc.typeartículo
dc.volumen38
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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