Profile monitoring for count data using Poisson and Conway-Maxwell-Poisson regression-based control charts under multicollinearity problem

In this paper, we propose new process control charts for monitoring Poisson and Conway-Maxwell-Poisson (COM-Poisson) profiles with highly correlated variables. We first propose an iterative ridge estimator for Poisson regression under multicollinearity and then modify it to COM-Poisson regression. After we define ridge deviance residuals which are approximately normal distributed, we construct Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) type control charts based on the ridge deviance residuals for monitoring both Poisson and COM-Poisson profiles. The performances of the proposed control charts are evaluated by using average run length criterion and the proposed control chart is compared to the existing method for monitoring the Poisson profiles through simulation study based on real historical data and COM-Poisson profile through a hypothetical data set. (C) 2020 Elsevier B.V. All rights reserved.