GLM-based control charts for the inverse Gaussian distributed response variable

In the modern era of digitalization, manufacturing industries needed monitoring methods to timely detect an abrupt change in the process. Control charts are widely used online monitoring method and used in several sectors for the surveillance of the process. Usually, control charts are developed for a single study variable, but there exists auxiliary information along with the study variable. Because of the linear relation between the study variable and auxiliary variable, several control chart studies are designed based on the simple linear regression model, but they are restricted to the normally distributed response variable. When the response variable follows an exponential family distribution, then the generalized linear modeling (GLM) approach provides better estimates. Hence, this study is designed to propose GLM-based control charts when the response variable follows the inverse Gaussian (IG) distribution. In GLM-based control charts, deviance and Pearson residuals of the IG regression are considered as plotting statistics. For the evaluation purpose, a simulation study is designed, and the performance of the proposed methods is compared with existing counterparts in terms of the run length properties. Moreover, run-rules are also implemented to gain the efficiency of the Shewhart type GLM-based control charts under small-to-moderate shifts. Finally, an example related to the yarn manufacturing industry is also used to highlight the importance of the stated proposal.