Weighted Score test based EWMA control charts for Zero-Inflated Poisson Models

Abstract

Zero-inflated Poisson models have been widely used to account for excess zero values in count data. Recent literature pointed out that the quality characteristic could be assumed to depend on a linear function of covariates in zero-inflated Poisson models, which is called risk-adjustment. Most existing approaches to monitoring zero-inflated Poisson processes mainly focus on parameter changes based on the observed response variable. The additional covariate information is not generally considered when monitoring the quality characteristic, even though this may cause significant information loss. In this research, we study an upper-sided exponentially weighted moving average control chart using a weighted score test statistic. The proposed control chart can detect the positive shifts in parameters of the Poisson part in zero-inflated Poisson models. Especially, this new method allows improving the capacity of detecting unnatural heterogeneity variability, thanks to the introduced random effect. Moreover, the simulation results via the Monte Carlo methodology are provided, which show that the proposed approach is more efficient than the existing PR-ZIP chart when detecting small to moderate shifts. Finally, the proposed chart is also applied to a practical example to demonstrate its utility.