Robust control charts via winsorized and trimmed estimators

In process control, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and synthetic control charts are developed to detect small and moderate shifts. Small shifts which are hard to detect can be costly to the process control if left undetected for a long period. These control cha...

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Main Author:	Ayu, Abdul Rahman
Format:	Thesis
Language:	eng eng eng
Published:	2020
Subjects:	QA273-280 Probabilities Mathematical statistics QA299.6-433 Analysis
Online Access:	https://etd.uum.edu.my/9837/1/permission%20to%20deposit-grant%20the%20permission-901746.pdf https://etd.uum.edu.my/9837/2/s901746_01.pdf https://etd.uum.edu.my/9837/3/references_901746.docx
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spelling	my-uum-etd.98372022-09-11T04:09:19Z Robust control charts via winsorized and trimmed estimators 2020 Ayu, Abdul Rahman Syed Yahaya, Sharipah Soaad Ali Atta, Abdu Mohammed Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Art & Sciences QA273-280 Probabilities. Mathematical statistics QA299.6-433 Analysis In process control, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and synthetic control charts are developed to detect small and moderate shifts. Small shifts which are hard to detect can be costly to the process control if left undetected for a long period. These control charts are not reliable under non-normality as the design structure of the charts is based on the sample mean. Sample mean is sensitive to outliers, a common cause of non-normality. In circumventing the problem, this study applied robust location estimators in the design structure of the control charts, instead of the sample mean. For such purpose, four robust estimators namely 20%-trimmed mean, median, modified one-step M-estimator (MOM), and winsorized MOM (WMOM) were chosen. The proposed charts were tested on several conditions which include sample sizes, shift sizes, and different types of non-normal distributions represented by the g-and-h distribution. Random variates for each distribution were obtained using SAS RANNOR before transforming them to the desired type of distribution. Robustness and detection ability of the charts were gauged through average run length (ARL) via simulation study. Validation of the charts’ performance which was done through real data study, specifically on potential diabetic patients at Universiti Utara Malaysia shows that robust EWMA chart and robust CUSUM chart outperform the standard charts. The findings concur with the results of simulation study. Even though robust synthetic chart is not among the best choice as it cannot detect small shifts as quickly as CUSUM or EWMA, its performance is much better than the standard chart under non-normality. This study reveals that all the proposed robust charts fare better than the standard charts under non-normality, and comparable with the latter under normality. The most robust among the investigated charts are EWMA control charts based on MOM and WMOM. These robust charts can fast detect small shifts regardless of distributional shapes and work well under small sample sizes. These characteristics suit the industrial needs in process monitoring. 2020 Thesis https://etd.uum.edu.my/9837/ https://etd.uum.edu.my/9837/1/permission%20to%20deposit-grant%20the%20permission-901746.pdf text eng staffonly https://etd.uum.edu.my/9837/2/s901746_01.pdf text eng public https://etd.uum.edu.my/9837/3/references_901746.docx text eng public other doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng eng
advisor	Syed Yahaya, Sharipah Soaad Ali Atta, Abdu Mohammed
topic	QA273-280 Probabilities Mathematical statistics QA299.6-433 Analysis
spellingShingle	QA273-280 Probabilities Mathematical statistics QA299.6-433 Analysis Ayu, Abdul Rahman Robust control charts via winsorized and trimmed estimators
description	In process control, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and synthetic control charts are developed to detect small and moderate shifts. Small shifts which are hard to detect can be costly to the process control if left undetected for a long period. These control charts are not reliable under non-normality as the design structure of the charts is based on the sample mean. Sample mean is sensitive to outliers, a common cause of non-normality. In circumventing the problem, this study applied robust location estimators in the design structure of the control charts, instead of the sample mean. For such purpose, four robust estimators namely 20%-trimmed mean, median, modified one-step M-estimator (MOM), and winsorized MOM (WMOM) were chosen. The proposed charts were tested on several conditions which include sample sizes, shift sizes, and different types of non-normal distributions represented by the g-and-h distribution. Random variates for each distribution were obtained using SAS RANNOR before transforming them to the desired type of distribution. Robustness and detection ability of the charts were gauged through average run length (ARL) via simulation study. Validation of the charts’ performance which was done through real data study, specifically on potential diabetic patients at Universiti Utara Malaysia shows that robust EWMA chart and robust CUSUM chart outperform the standard charts. The findings concur with the results of simulation study. Even though robust synthetic chart is not among the best choice as it cannot detect small shifts as quickly as CUSUM or EWMA, its performance is much better than the standard chart under non-normality. This study reveals that all the proposed robust charts fare better than the standard charts under non-normality, and comparable with the latter under normality. The most robust among the investigated charts are EWMA control charts based on MOM and WMOM. These robust charts can fast detect small shifts regardless of distributional shapes and work well under small sample sizes. These characteristics suit the industrial needs in process monitoring.
format	Thesis
qualification_name	other
qualification_level	Doctorate
author	Ayu, Abdul Rahman
author_facet	Ayu, Abdul Rahman
author_sort	Ayu, Abdul Rahman
title	Robust control charts via winsorized and trimmed estimators
title_short	Robust control charts via winsorized and trimmed estimators
title_full	Robust control charts via winsorized and trimmed estimators
title_fullStr	Robust control charts via winsorized and trimmed estimators
title_full_unstemmed	Robust control charts via winsorized and trimmed estimators
title_sort	robust control charts via winsorized and trimmed estimators
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2020
url	https://etd.uum.edu.my/9837/1/permission%20to%20deposit-grant%20the%20permission-901746.pdf https://etd.uum.edu.my/9837/2/s901746_01.pdf https://etd.uum.edu.my/9837/3/references_901746.docx
_version_	1747828684753993728

Robust control charts via winsorized and trimmed estimators

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