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

Abstract

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.

Memory type control charts with inverse-Gaussian response: An application to yarn manufacturing industry

“…In the case of the univariate response variable, the DR of the IG regression are described as (Kinat et al, 2020)…”

“…Kinat et al (2020) proposed memory less GLM-based control charts on the basis of DR and PR when the response variable follows an IG distribution. These charts are discussed in the following subsections.…”

“…Recently, Kinat et al (2020) proposed Phase II type memory less GLM-based control charts on the basis of DR and Pearson residuals (PR) when the response variable follows an inverse Gaussian (IG) distribution. These charts are useful for detecting large shifts in the mean of IG response variable.…”

Auxiliary‐information‐based efficient variability control charts for Phase I of SPC

“…The two well-known measures for evaluating control charts' performance are average run length (ARL) and probability to signal (PTS). ARL is well suited for Phase II control charts, [41][42][43][44][45] while for Phase I charts, one is mostly interested in the probability of detecting inconsistent/contaminated samples (or observations). 29,46 Hence, in this study, PTS is used to compare the performance of the charts in Phase I.…”

New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data

“…The most common maximum likelihood estimation (MLE) is used to estimate the regression coefficients of the IGRM. The applications of IGRM are mostly observed in the fields of physical sciences, health sciences, chemical sciences, and engineering (Amin, Amanullah, and Aslam 2016;Kinat, Amin, and Mahmood 2020;Akram, Amin, and Qasim 2020;Naveed et al 2020;Amin, Amanullah, and Qasim 2020). Multicollinearity is an imperative problem particularly in fields of chemometrics, health sciences, and biostatistics.…”