GLM-based statistical control r-charts for dispersed count data with multicollinearity between input variables

The Poisson distribution is commonly used to describe count data for a control chart. However, it may not be appropriate for overdispersion or underdispersion. Thus, it is necessary to generalize the control chart to work well in such situations. This paper proposes a strategy for monitoring dispersed count data with multicollinearity between input variables by combining generalized linear model and principal component analysis. In the strategy, the generalized linear model using flexible distributions is performed on principal component scores from principal component analysis. The deviance residuals from the fitted model are then used to monitor the process. Simulation is conducted for performance under various situations. Also, a real dataset that is not suitable for a classical control chart is used in our example. The results from the simulated data and real data example support our proposed method.