New statistical process control charts for overdispersed count data based on the Bell distribution

Abstract

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.