Generalized likelihood ratio based risk-adjusted control chart for zero-inflated Poisson process

Nowadays, statistical process control has been widely used to monitor processes in various fields. To monitor processes with a large number of zero observations by control charts, the zero-inflated Poisson (ZIP) model has been adopted. Due to the heterogeneity of each sample in the process, several factors have been taken into account to predict values of two parameters in the ZIP model by risk adjustment. Instead of considering two parameters to be constant directly, risk-adjusted ZIP control charts can provide more reasonable monitoring results than traditional ones. However, existing methods ignored the interaction between parameters in the ZIP model, which leads to some risk-adjusted control charts unable to accurately estimate parameters to provide effective monitoring results. To address this problem, this paper presents a generalize likelihood ratio (GLR) based control chart to better monitor the risk-adjusted ZIP process with EWMA scheme, which can detect the random shift in both parameters efficiently. In the simulation study, the proposed control chart is compared with another two existing control charts and shows superior performance on detecting various types of shifts in parameters. Finally, the proposed control chart is applied to the Hong Kong influenza datasets and the flight delay datasets to illustrate its effectiveness and utility.