| Full text | |
| Author(s): |
Jesus, Bruno D.
;
Ferreira, Paulo H.
;
Boaventura, Laion L.
;
Fiaccone, Rosemeire L.
;
Bertoli, Wesley
;
Ramos, Pedro L.
;
Louzada, Francisco
Total Authors: 7
|
| Document type: | Journal article |
| Source: | QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL; v. N/A, p. 21-pg., 2022-02-08. |
| Abstract | |
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) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/25971-0 - Statistical inference of complex systems |
| Grantee: | Pedro Luiz Ramos |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |