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

Autor(es)

Jesus, Bruno D. ; Ferreira, Paulo H. ; Boaventura, Laion L. ; Fiaccone, Rosemeire L. ; Bertoli, Wesley ; Ramos, Pedro L. ; Louzada, Francisco

• Tipo de documento: Artigo Científico
• Fonte: QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL; v. N/A, p. 21-pg., 2022-02-08.

Resumo

The 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. (AU)

• Processo FAPESP: 13/07375-0 - CeMEAI - Centro de Ciências Matemáticas Aplicadas à Indústria
• Beneficiário: Francisco Louzada Neto
• Modalidade de apoio: Auxílio à Pesquisa - Centros de Pesquisa, Inovação e Difusão - CEPIDs
• Processo FAPESP: 17/25971-0 - Inferência estatística de sistemas complexos
• Beneficiário: Pedro Luiz Ramos
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado