Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring
In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity...
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/6/455 |
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| author | Muhammad Amin Samra Rani Sadiah M. A. Aljeddani |
| author_facet | Muhammad Amin Samra Rani Sadiah M. A. Aljeddani |
| author_sort | Muhammad Amin |
| collection | DOAJ |
| description | In manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control charts become unreliable. This study introduces novel Shewhart control charts using Pearson and deviance residuals based on the inverse Gaussian ridge regression (IGRR) model to address this issue. The proposed IGRR-based charts effectively handle multicollinearity, offering a robust alternative for process monitoring. Their performance is evaluated through Monte Carlo simulations using average run length (<i>ARL</i>) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and <i>MLE</i>-based methods, particularly under high multicollinearity. A real-world application to a Pakistan air quality dataset confirms their superior sensitivity in detecting pollution spikes, enabling timely environmental negotiations. These findings establish Pearson residual-based IGRR control charts as a practical and reliable tool for monitoring complex processes with correlated variables. |
| format | Article |
| id | doaj-art-c0b5ce065e5843fe84bbe58deaed1c02 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c0b5ce065e5843fe84bbe58deaed1c022025-08-20T02:24:18ZengMDPI AGAxioms2075-16802025-06-0114645510.3390/axioms14060455Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality MonitoringMuhammad Amin0Samra Rani1Sadiah M. A. Aljeddani2Department of Statistics, University of Sargodha, Sargodha 40100, PakistanDepartment of Statistics, Government Graduate College Bhalwal, Sargodha 40100, PakistanMathematics Department, Al-Lith University College, Umm Al-Qura University, Al-Lith 21961, Saudi ArabiaIn manufacturing and service industries, monitoring processes with correlated input variables and inverse Gaussian (IG)-distributed quality characteristics is challenging due to the limitations of maximum likelihood estimator (MLE)-based control charts. When input variables exhibit multicollinearity, traditional MLE-based inverse Gaussian regression model (IGRM) control charts become unreliable. This study introduces novel Shewhart control charts using Pearson and deviance residuals based on the inverse Gaussian ridge regression (IGRR) model to address this issue. The proposed IGRR-based charts effectively handle multicollinearity, offering a robust alternative for process monitoring. Their performance is evaluated through Monte Carlo simulations using average run length (<i>ARL</i>) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and <i>MLE</i>-based methods, particularly under high multicollinearity. A real-world application to a Pakistan air quality dataset confirms their superior sensitivity in detecting pollution spikes, enabling timely environmental negotiations. These findings establish Pearson residual-based IGRR control charts as a practical and reliable tool for monitoring complex processes with correlated variables.https://www.mdpi.com/2075-1680/14/6/455air qualityARLcontrol chartsinverse Gaussian regressionPearson residualsdeviance residuals |
| spellingShingle | Muhammad Amin Samra Rani Sadiah M. A. Aljeddani Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring Axioms air quality ARL control charts inverse Gaussian regression Pearson residuals deviance residuals |
| title | Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring |
| title_full | Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring |
| title_fullStr | Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring |
| title_full_unstemmed | Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring |
| title_short | Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring |
| title_sort | pearson and deviance residual based control charts for the inverse gaussian ridge regression process simulation and an application to air quality monitoring |
| topic | air quality ARL control charts inverse Gaussian regression Pearson residuals deviance residuals |
| url | https://www.mdpi.com/2075-1680/14/6/455 |
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