Residuals based EWMA control charts with risk adjustments for zero-inflated Poisson models

Count data are widely available in many fields and numerous studies have designed control charts for them to monitor count processes. However, these control charts have limited effect on the "zero-inflated" data who have excess zeros. Zero-inflated Poisson (ZIP) models are important methods to deal with the data and some control charts based on them have been proposed. Unfortunately, there are still some limitations in these works, such as lack of risk adjustments, inability to monitor two parameters of ZIP models simultaneously, or insufficient sensitivity to small shifts. Therefore, in this paper, we propose residuals based exponentially weighted moving average (EWMA) control charts with risk adjustments for ZIP models to detect small shifts in zero-inflated data. With taking Pearson and deviance residuals as targets, the two parameters can be monitored simultaneously. The results of simulation study via Monte Carlo methodology demonstrate that our charts have better performance than the existing charts in detecting the small changes of zero-inflated processes. In addition, according to the results, we advise that it is best to use the EWMA chart based on deviance residuals (DR-EWMA) to obtain the optimal monitoring performance when the likelihood function is easy to define; otherwise, that based on Pearson residuals (PR-EWMA) can still provide better results than the existing charts. Finally, two different real data sets are used to verify the practicability of our charts.