Likelihood-based control chart with the EWMA scheme for zero-inflated Poisson models

Recently, control chart methods for monitoring risk-adjusted zero-inflated Poisson (RA-ZIP) processes have gained attention. Existing approaches often assume a constant shock probability pi and ignore cumulative sample information when estimating model parameters, reducing sensitivity to process shifts. This study proposes a likelihood-based EWMA-type control chart for detecting upward or downward shifts in both the Poisson mean θi and the shock probability pi in RA-ZIP profiles. A memory-type scheme updates the maximum likelihood estimators of the regression parameters from ZIP samples, and a weighted likelihood ratio test (WLRT) statistic is constructed. Monte Carlo simulations compare the proposed WLRT chart with existing WST and GLR charts using the average run length, run length standard deviation, and the relative mean index. The proposed chart shows competitive and often superior sensitivity, particularly for small regression-structure shifts. An application to US flight delay data demonstrates its practical implementation.