Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Sta...

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Autores principales:	Ishaq Adeyanju Raji, Nasir Abbas, Mu’azu Ramat Abujiya, Muhammad Riaz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	multivariate control charts Mahalanobis distance control chart Hotelling <i>T</i><sup>2</sup> Stahel-Donoho robust estimators outlier detection Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/019af6214df847268c26ff700449f57d
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spelling	oai:doaj.org-article:019af6214df847268c26ff700449f57d2021-11-11T18:18:51ZRobust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection10.3390/math92127722227-7390https://doaj.org/article/019af6214df847268c26ff700449f57d2021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2772https://doaj.org/toc/2227-7390While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling <i>T</i><sup>2</sup> chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.Ishaq Adeyanju RajiNasir AbbasMu’azu Ramat AbujiyaMuhammad RiazMDPI AGarticlemultivariate control chartsMahalanobis distancecontrol chartHotelling <i>T</i><sup>2</sup>Stahel-Donoho robust estimatorsoutlier detectionMathematicsQA1-939ENMathematics, Vol 9, Iss 2772, p 2772 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	multivariate control charts Mahalanobis distance control chart Hotelling <i>T</i><sup>2</sup> Stahel-Donoho robust estimators outlier detection Mathematics QA1-939
spellingShingle	multivariate control charts Mahalanobis distance control chart Hotelling <i>T</i><sup>2</sup> Stahel-Donoho robust estimators outlier detection Mathematics QA1-939 Ishaq Adeyanju Raji Nasir Abbas Mu’azu Ramat Abujiya Muhammad Riaz Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
description	While researchers and practitioners may seamlessly develop methods of detecting outliers in control charts under a univariate setup, detecting and screening outliers in multivariate control charts pose serious challenges. In this study, we propose a robust multivariate control chart based on the Stahel-Donoho robust estimator (SDRE), whilst the process parameters are estimated from phase-I. Through intensive Monte-Carlo simulation, the study presents how the estimation of parameters and presence of outliers affect the efficacy of the Hotelling <i>T</i><sup>2</sup> chart, and then how the proposed outlier detector brings the chart back to normalcy by restoring its efficacy and sensitivity. Run-length properties are used as the performance measures. The run length properties establish the superiority of the proposed scheme over the default multivariate Shewhart control charting scheme. The applicability of the study includes but is not limited to manufacturing and health industries. The study concludes with a real-life application of the proposed chart on a dataset extracted from the manufacturing process of carbon fiber tubes.
format	article
author	Ishaq Adeyanju Raji Nasir Abbas Mu’azu Ramat Abujiya Muhammad Riaz
author_facet	Ishaq Adeyanju Raji Nasir Abbas Mu’azu Ramat Abujiya Muhammad Riaz
author_sort	Ishaq Adeyanju Raji
title	Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
title_short	Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
title_full	Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
title_fullStr	Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
title_full_unstemmed	Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection
title_sort	robust multivariate shewhart control chart based on the stahel-donoho robust estimator and mahalanobis distance for multivariate outlier detection
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/019af6214df847268c26ff700449f57d
work_keys_str_mv	AT ishaqadeyanjuraji robustmultivariateshewhartcontrolchartbasedonthestaheldonohorobustestimatorandmahalanobisdistanceformultivariateoutlierdetection AT nasirabbas robustmultivariateshewhartcontrolchartbasedonthestaheldonohorobustestimatorandmahalanobisdistanceformultivariateoutlierdetection AT muazuramatabujiya robustmultivariateshewhartcontrolchartbasedonthestaheldonohorobustestimatorandmahalanobisdistanceformultivariateoutlierdetection AT muhammadriaz robustmultivariateshewhartcontrolchartbasedonthestaheldonohorobustestimatorandmahalanobisdistanceformultivariateoutlierdetection
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Robust Multivariate Shewhart Control Chart Based on the Stahel-Donoho Robust Estimator and Mahalanobis Distance for Multivariate Outlier Detection

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