Deviance residual-based Shewhart control chart for monitoring Conway-Maxwell-Poisson profile under the r-k class estimator

Abstract

ABSTRACTIn this study, we first propose the r-k class estimator in COM-Poisson regression, and then we introduce the Shewhart control chart using the deviance residuals obtained from the r-k class estimator. The performance analysis of the new control chart over maximum likelihood, principal components regression, and ridge-based Shewhart control charts is evaluated via a numerical example and a simulation study by using average run length, the standard deviation of run length, the average alarm rate and percentile of run length criteria when different types of shifts are present in data.KEYWORDS: Conway-Maxwell-Poisson distributionprincipal component regressionprofile monitoringridge estimatorresidual control chartpercentile AcknowledgementsThis work was supported by the Research Fund of Çukurova University, Turkey under Project Number FDK-2019-11935.Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1. If the projection matrix is not idempotent, it is called as quasi-projection matrix (Tripp, Citation1983; Özkale, Citation2013).2. The data set is available in the ‘CountsEPPM’ (Smith & Faddy, Citation2018) package.3. specifically ‘xshewhartrunsrules.crit’ function4. Bold in the table shows the optimum value.Additional informationFundingThis work was supported by the Çukurova Üniversitesi [FDK-2019-11935].Notes on contributorsUlduz MammadovaUlduz Mammadova received her Ph.D. degree in Statistics from Çukurova University, Turkey. Her main research interests are Applied Statistics, Statistical Quality Control, and Regression Analysis.M.Revan ÖzkaleM. Revan Özkale received M.S. and Ph.D. degrees in Statistics from Çukurova University in 2004 and 2007, respectively. She is a full professor at the Department of Statistics, Çukurova University. Her research interest includes Regression Analysis, Machine Learning, High Dimensional Data, Generalized Linear Models, Linear Mixed Models, Shrinkage Estimation, and Statistical Quality Control.