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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:English
English
English
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
https://etd.uum.edu.my/9837/
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spelling my.uum.etd.98372022-09-11T04:09:19Z https://etd.uum.edu.my/9837/ Robust control charts via winsorized and trimmed estimators Ayu, Abdul Rahman 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 NonPeerReviewed text en https://etd.uum.edu.my/9837/1/permission%20to%20deposit-grant%20the%20permission-901746.pdf text en https://etd.uum.edu.my/9837/2/s901746_01.pdf text en https://etd.uum.edu.my/9837/3/references_901746.docx Ayu, Abdul Rahman (2020) Robust control charts via winsorized and trimmed estimators. Doctoral thesis, Universiti Utara Malaysia.
institution Universiti Utara Malaysia
building UUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Utara Malaysia
content_source UUM Electronic Theses
url_provider http://etd.uum.edu.my/
language English
English
English
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
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
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
https://etd.uum.edu.my/9837/
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score 13.211869

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