Statistical Process Control Using Modified Robust Hotelling's T² Control Charts

Hotelling’s T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive to outliers. To alleviate the problem, three approaches to the robust Hotelling’s T² chart namely trimming, Winsorizing and median based were proposed. These approaches used robust loc...

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Main Author:	Haddad, Firas Saleem Fares
Format:	Thesis
Language:	eng eng
Published:	2013
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	https://etd.uum.edu.my/3865/1/s90825.pdf https://etd.uum.edu.my/3865/7/s90825.pdf
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id	my-uum-etd.3865
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Syed Yahaya, Sharipah Soaad
topic	QA273-280 Probabilities Mathematical statistics
spellingShingle	QA273-280 Probabilities Mathematical statistics Haddad, Firas Saleem Fares Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
description	Hotelling’s T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive to outliers. To alleviate the problem, three approaches to the robust Hotelling’s T² chart namely trimming, Winsorizing and median based were proposed. These approaches used robust location and scale estimators to substitute for the usual mean and covariance matrix, respectively. For each approach, three robust scale estimators: MADn, Sn and Tn were introduced, and these estimators functioned accordingly to the approach. The first approach, denoted as T²t, applied the concept of trimming via Mahalanobis distance. The robust scale estimator was used to replace the covariance matrix in Mahalanobis distance. The trimmed mean and trimmed covariance matrix were the location and scale estimators for the T²t chart. The second approach,, T²w, employed each scale estimator as the Winsorized criterion. This approach applied Winsorized modified one step M-estimator and its corresponding Winsorized covariance as the location and the scale matrix for T²w chart, respectively. Meanwhile, in the third approach, T²н, the robust scale estimator took the role of the scale matrix with Hodges-Lehman as the location estimator. This approach worked with the original data without any trimming or Winsorizing. Altogether, nine robust control charts were proposed. The performance of each robust control chart was assessed based on false alarm rates and probability of detection. To investigate on the strengths and weaknesses of the proposed charts, various conditions were created by manipulating four variables, namely number of quality characteristics, proportion of outliers, degree of mean shifts, and nature of quality characteristics (independent and dependent). In general, the proposed charts performed well in terms of false alarm rates. With respect to probability of detection, all the proposed charts outperformed the traditional Hotelling's T² charts. The overall findings showed that, the proposed robust Hotelling's T² control charts are viable alternatives to the disputed traditional charts.
format	Thesis
qualification_name	Ph.D.
qualification_level	Doctorate
author	Haddad, Firas Saleem Fares
author_facet	Haddad, Firas Saleem Fares
author_sort	Haddad, Firas Saleem Fares
title	Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
title_short	Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
title_full	Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
title_fullStr	Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
title_full_unstemmed	Statistical Process Control Using Modified Robust Hotelling's T² Control Charts
title_sort	statistical process control using modified robust hotelling's t² control charts
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2013
url	https://etd.uum.edu.my/3865/1/s90825.pdf https://etd.uum.edu.my/3865/7/s90825.pdf
_version_	1747827657184116736
spelling	my-uum-etd.38652022-09-19T08:02:18Z Statistical Process Control Using Modified Robust Hotelling's T² Control Charts 2013 Haddad, Firas Saleem Fares Syed Yahaya, Sharipah Soaad Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Hotelling’s T² chart is a popular tool for monitoring statistical process control. However, this chart is sensitive to outliers. To alleviate the problem, three approaches to the robust Hotelling’s T² chart namely trimming, Winsorizing and median based were proposed. These approaches used robust location and scale estimators to substitute for the usual mean and covariance matrix, respectively. For each approach, three robust scale estimators: MADn, Sn and Tn were introduced, and these estimators functioned accordingly to the approach. The first approach, denoted as T²t, applied the concept of trimming via Mahalanobis distance. The robust scale estimator was used to replace the covariance matrix in Mahalanobis distance. The trimmed mean and trimmed covariance matrix were the location and scale estimators for the T²t chart. The second approach,, T²w, employed each scale estimator as the Winsorized criterion. This approach applied Winsorized modified one step M-estimator and its corresponding Winsorized covariance as the location and the scale matrix for T²w chart, respectively. Meanwhile, in the third approach, T²н, the robust scale estimator took the role of the scale matrix with Hodges-Lehman as the location estimator. This approach worked with the original data without any trimming or Winsorizing. Altogether, nine robust control charts were proposed. The performance of each robust control chart was assessed based on false alarm rates and probability of detection. To investigate on the strengths and weaknesses of the proposed charts, various conditions were created by manipulating four variables, namely number of quality characteristics, proportion of outliers, degree of mean shifts, and nature of quality characteristics (independent and dependent). In general, the proposed charts performed well in terms of false alarm rates. With respect to probability of detection, all the proposed charts outperformed the traditional Hotelling's T² charts. The overall findings showed that, the proposed robust Hotelling's T² control charts are viable alternatives to the disputed traditional charts. 2013 Thesis https://etd.uum.edu.my/3865/ https://etd.uum.edu.my/3865/1/s90825.pdf text eng public https://etd.uum.edu.my/3865/7/s90825.pdf text eng public Ph.D. doctoral Universiti Utara Malaysia Abu-Shawiesh, M. O. & Abdullah, M. (2001). A new Robust Bivariate Control Chart For Location. Communication in statistics, 30, 513–529. Alfaro, J. L. & Ortega, J. F. 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Statistical Process Control Using Modified Robust Hotelling's T² Control Charts

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