{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:21:46Z","timestamp":1760059306886,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T00:00:00Z","timestamp":1749427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006701","name":"Umm Al-Qura University","doi-asserted-by":"publisher","award":["25UQU4310037GSSR07"],"award-info":[{"award-number":["25UQU4310037GSSR07"]}],"id":[{"id":"10.13039\/501100006701","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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 (ARL) as the main criteria, demonstrating that Pearson residual-based IGRR charts outperform deviance residual-based charts and MLE-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.<\/jats:p>","DOI":"10.3390\/axioms14060455","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T08:22:34Z","timestamp":1749457354000},"page":"455","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Pearson and Deviance Residual-Based Control Charts for the Inverse Gaussian Ridge Regression Process: Simulation and an Application to Air Quality Monitoring"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7431-5756","authenticated-orcid":false,"given":"Muhammad","family":"Amin","sequence":"first","affiliation":[{"name":"Department of Statistics, University of Sargodha, Sargodha 40100, Pakistan"}]},{"given":"Samra","family":"Rani","sequence":"additional","affiliation":[{"name":"Department of Statistics, Government Graduate College Bhalwal, Sargodha 40100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6581-0758","authenticated-orcid":false,"given":"Sadiah M. A.","family":"Aljeddani","sequence":"additional","affiliation":[{"name":"Mathematics Department, Al-Lith University College, Umm Al-Qura University, Al-Lith 21961, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00224065.1969.11980341","article-title":"The Regression Control Chart","volume":"1","author":"Mandel","year":"1969","journal-title":"J. Qual. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1002\/qre.521","article-title":"Process Monitoring for Correlated Gamma-Distributed Data Using Generalized-Linear-Model-Based Control Charts","volume":"19","author":"Jearkpaporn","year":"2003","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1080\/00224065.2000.11980027","article-title":"On-Line Monitoring When the Process Yields a Linear Profile","volume":"32","author":"Kang","year":"2000","journal-title":"J. Qual. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/08982119308918998","article-title":"The Statistical Design of CUSUM Charts","volume":"5","author":"Woodall","year":"1993","journal-title":"Qual. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1002\/qre.711","article-title":"Using Profile Monitoring Techniques for a Data-Rich Environment with Huge Sample Size","volume":"21","author":"Wang","year":"2005","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_6","first-page":"233","article-title":"A Generalized Linear Statistical Model Approach to Monitor Profiles","volume":"20","author":"Niaki","year":"2007","journal-title":"Int. J. Eng."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1080\/00207540210163964","article-title":"Process Monitoring for Multiple Count Data Using Generalized Linear Model-Based Control Charts","volume":"41","author":"Skinner","year":"2003","journal-title":"Int. J. Prod. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"777","DOI":"10.1002\/qre.603","article-title":"Generalized Linear Model-Based Control Charts for Discrete Semiconductor Process Data","volume":"20","author":"Skinner","year":"2004","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1080\/16843703.2016.1189013","article-title":"Monitoring Two-Stage Processes with Binomial Data Using Generalized Linear Model-Based Control Charts","volume":"13","author":"Amiri","year":"2016","journal-title":"Qual. Technol. Quant. Manag."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2839","DOI":"10.1080\/00949655.2014.942864","article-title":"Phase I Monitoring of Generalized Linear Model-Based Regression Profiles","volume":"85","author":"Amiri","year":"2015","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1080\/03610918.2014.970698","article-title":"A Change Point Method for Phase II Monitoring of Generalized Linear Profiles","volume":"46","author":"Shadman","year":"2017","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_12","first-page":"1078","article-title":"Regression Control Charts\u2014A Survey","volume":"14","author":"Nancy","year":"2023","journal-title":"J. Pharm. Negat. Results"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1103","DOI":"10.1002\/qre.2310","article-title":"GLM-Based Statistical Control r-Charts for Dispersed Count Data with Multicollinearity between Input Variables","volume":"34","author":"Park","year":"2018","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Kim, J.M., Wang, N., Liu, Y., and Park, K. (2020). Residual Control Chart for Binary Response with Multicollinearity Covariates by Neural Network Model. Symmetry, 12.","DOI":"10.3390\/sym12030381"},{"key":"ref_15","unstructured":"Mammadova, U., and Revan, M. (2025, April 16). Generalized Linear Model-Based Regression Control Chart with Poisson Response. Available online: https:\/\/fbe.cu.edu.tr\/storage\/fbeyedek\/makaleler\/2017\/GENERALIZED%20LINEAR%20MODEL.pdf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"287","DOI":"10.18576\/isl\/110129","article-title":"Performance Comparison of Residual Control Charts for a Count Data Based on Ridge Regression","volume":"11","author":"Yassin","year":"2022","journal-title":"Inf. Sci. Lett."},{"key":"ref_17","first-page":"164","article-title":"Shewhart Control Chart of Poisson Regression under Ridge Regression","volume":"3","author":"Mohammed","year":"2023","journal-title":"World Res. Bus. Adm. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1080\/03610918.2020.1870693","article-title":"Comparison of Deviance and Ridge Deviance Residual-Based Control Charts for Monitoring Poisson Profiles","volume":"52","author":"Mammadova","year":"2023","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_19","unstructured":"Nancy, M., and Joshi, H. (2022, January 13\u201315). Tracking Sigmoid Regression with Multicollinearity in Phase I: An Approach Incorporating Control Charts. Proceedings of the International Conference on Statistics and Data Science, Lisbon, Portugal."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s00362-023-01399-z","article-title":"Detecting Shifts in Conway\u2013Maxwell\u2013Poisson Profile with Deviance Residual-Based CUSUM and EWMA Charts under Multicollinearity","volume":"65","author":"Mammadova","year":"2024","journal-title":"Stat. Pap."},{"key":"ref_21","first-page":"121","article-title":"Conway\u2013Maxwell\u2013Poisson Profile Monitoring with rk-Shewhart Control Chart: A Comparative Study","volume":"57","author":"Mammadova","year":"2024","journal-title":"J. Sci. Rep. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1080\/00949655.2023.2299354","article-title":"Shewhart Ridge Profiling for the Gamma Response Model","volume":"94","author":"Aslam","year":"2024","journal-title":"J. Stat. Comput. Simul."},{"key":"ref_23","first-page":"289","article-title":"Zur Theorie der Fall- und Steigversuche an Teilchen mit Brownscher Bewegung","volume":"16","year":"1915","journal-title":"Phys. Z."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1038\/155453a0","article-title":"Inverse Statistical Variates","volume":"155","author":"Tweedie","year":"1945","journal-title":"Nature"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1111\/j.1467-842X.1989.tb00500.x","article-title":"Inverse Gaussian Control Charts","volume":"31","author":"Edgeman","year":"1989","journal-title":"Aust. J. Stat."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hardin, J.W., and Hilbe, J.M. (2012). Generalized Estimating Equations, Chapman and Hall\/CRC.","DOI":"10.1201\/b13880"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1111\/j.2517-6161.1984.tb01288.x","article-title":"Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and Some Robust and Resistant Alternatives","volume":"46","author":"Green","year":"1984","journal-title":"J. R. Stat. Soc. Ser. B Methodol."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","article-title":"Ridge regression: Biased estimation for nonorthogonal problems","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6170","DOI":"10.1080\/03610918.2020.1797794","article-title":"New Ridge Estimators in the Inverse Gaussian Regression: Monte Carlo Simulation and Application to Chemical Data","volume":"51","author":"Amin","year":"2022","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/cem.2805","article-title":"Empirical Evaluation of the Inverse Gaussian Regression Residuals for the Assessment of Influential Points","volume":"30","author":"Amin","year":"2016","journal-title":"J. Chemom."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1177\/0142331220952965","article-title":"Memory Type Control Charts with Inverse-Gaussian Response: An Application to Yarn Manufacturing Industry","volume":"43","author":"Amin","year":"2021","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1002\/qre.2603","article-title":"GLM-Based Control Charts for the Inverse Gaussian Response Variable","volume":"36","author":"Kinat","year":"2020","journal-title":"Qual. Reliab. Eng. Int."},{"key":"ref_33","unstructured":"Montgomery, D.C. (2008). Introduction to Statistical Quality Control, Wiley. [6th ed.]."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s10614-011-9275-x","article-title":"Performance of Some Logistic Ridge Regression Estimators","volume":"40","author":"Kibria","year":"2012","journal-title":"Comput. Econ."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"495","DOI":"10.32614\/RJ-2016-062","article-title":"mctest: An R package for detection of collinearity among regressors","volume":"8","author":"Imdadullah","year":"2016","journal-title":"R. J."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/455\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:48:53Z","timestamp":1760032133000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/6\/455"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,9]]},"references-count":35,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["axioms14060455"],"URL":"https:\/\/doi.org\/10.3390\/axioms14060455","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,6,9]]}}}