Statistical process control of over-dispersed multivariate count data

Statistical process control of multi-attribute data has received much attention. However, little work has been done on over-dispersed multivariate count data with either positive or negative correlations. In this article, we focus on designing a new control scheme for such kind of data. The new method models the data with the Poisson Log-normal distribution and monitors the process with Hotelling T² control chart. The parameter estimation is achieved via Quasi-Newton algorithm. The limitation of some existing multi-attribute control charts in presence of over-dispersion is also shown. Furthermore, the performance of the new control chart is evaluated by Monte Carlo simulation.