Browsing by Author "Boaventura, Laion L."

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    New statistical process control charts for overdispersed count data based on the Bell distribution
    (2023) Boaventura, Laion L.; Ferreira, Paulo H.; Fiaccone, Rosemeire L.; Ramos, Pedro L.; Louzada, Francisco
    Poisson distribution is a popular discrete model used to describe counting information, from which traditional control charts involving count data, such as the c and u charts, have been established in the literature. However, several studies recognize the need for alternative control charts that allow for data overdispersion, which can be encountered in many fields, including ecology, healthcare, industry, and others. The Bell distribution, recently proposed by Castellares et al. (2018), is a particular solution of a multiple Poisson process able to accommodate overdispersed data. It can be used as an alternative to the usual Poisson (which, although not nested in the Bell family, is approached for small values of the Bell distribution) Poisson, negative binomial, and COM-Poisson distributions for modeling count data in several areas. In this paper, we consider the Bell distribution to introduce two new exciting, and useful statistical control charts for counting processes, which are capable of monitoring count data with overdispersion. The performance of the so-called Bell charts, namely Bell-c and Bell-u charts, is evaluated by the average run length in numerical simulation. Some artificial and real data sets are used to illustrate the applicability of the proposed control charts.
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    Statistical process control of overdispersed count data based on one-parameter Poisson mixture models
    (2022) Jesus, Bruno D.; Ferreira, Paulo H.; Boaventura, Laion L.; Fiaccone, Rosemeire L.; Bertoli, Wesley; Ramos, Pedro L.; Louzada, Francisco
    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.