An optimal multivariate control chart for correlated Poisson variables using multiple dependent state sampling

In this article we propose a control chart to monitor correlated Poisson variables, which uses a statistic based on the linear combination of Poisson variables considering the methodology of sampling called Multiple Dependent State. In order to analyse the performance of this chart, a friendly software has been developed, which finds the best parameters to optimise the out-of-control average run length (ARL) for a shift that the practitioner wishes to detect as quickly as possible, restricted to a fixed value of in-control ARL. Additionally, some scenarios have been considered in the comparison of performance and a sensitivity analysis was carried out. The results show that the MDSLCP chart has better performance than the LCP chart.