Conway–Maxwell Poisson regression‐based control charts under iterative Liu estimator for monitoring count data

Abstract

AbstractDuring the evaluation and monitoring of a process, shifts are inherit parts of any statistical process control. In statistical process control, identifying the sources of such shifts is essential. Although there are many tools to identify the sources of such shifts, the control charts are most commonly used to identify these shifts. In this article, Shewhart, CUSUM, and EWMA control charts are proposed based on Liu deviance residuals for count data when there is a multicollinearity problem in Conway–Maxwell Poisson profiles to identify shifts. The comparisons of the proposed control charts are made with the deviance and ridge deviance‐based Shewhart, CUSUM, and EWMA control charts. Thus, a numerical illustration through bike‐sharing dataset and Monte Carlo simulation are considered. The simulation study is performed for the Poisson and COM‐Poisson distributions to see the effects of over‐ and underdispersion, the number of predictors as well as the shift size.