A change point method for monitoring generalized linear profiles in Phase I

In Phase I monitoring problems for generalized linear models, we assume that Poisson functional data with fixed samples collected over time follows a generalized linear model. Subsequently, we propose the likelihood ratio function of the change-point method, combined with constructing Exponentially Weighted Moving Average (EWMA) statistic, to monitor generalized linear models where parameters are undisclosed but can be approximated using historical data. Through numerous numerical simulations, we have derived the control limits and achieved the desired Average Run Length (ARL).