On the Modelling and Monitoring of General Inflated Poisson Processes

In this work, we propose and study general inflated probability distributions that can be used for modelling and monitoring unusual count data. The considered models extend the well‐known zero‐inflated Poisson distribution because they allow the excess of values, other than zero. Four simple upper‐sided control schemes are considered for the monitoring of count data based on the proposed general inflated Poisson distributions, and their performance is evaluated under various out‐of‐control situations. The usefulness of the considered models and techniques is illustrated via two real‐data examples, while practical guidelines are provided as well.