An MLE approach for estimating the time of step changes in Poissonregression profiles

In some process control applications, the quality of a product or process can be characterized by a relationship between two or more variables, which is typically referred to as a profile. Moreover, in some situations, the dependent variable is a count, which can be modeled as a Poisson regression of one explanatory variable. We refer to this as Poisson regression profiles. Control chart signals do not indicate the real time of process changes, so estimators are applied to indicate the time when a change in the process takes place, which is referred to as the change point. In this paper, we propose the use of an MLE estimator to identify the real time of a step change in phase II monitoring of Poisson regression profiles. The results reveal that the change point estimator is effective in identifying step shifts in the process parameters.