Monitoring process variability with symmetric control limits

Control charts for monitoring process variability, such as the R-chart and S-chart, do not have symmetric probability limits as the distribution of the sample variability is not normal. Hence, the usual zone rules can not be applied although it is still desirable to be able to use the information fr...

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Main Author: YANG, Zhenlin
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Language:English
Published: Institutional Knowledge at Singapore Management University 2002
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Online Access:https://ink.library.smu.edu.sg/soe_research/2064
https://ink.library.smu.edu.sg/context/soe_research/article/3063/viewcontent/YangXie2002.pdf
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spelling sg-smu-ink.soe_research-30632017-08-31T02:57:53Z Monitoring process variability with symmetric control limits YANG, Zhenlin Control charts for monitoring process variability, such as the R-chart and S-chart, do not have symmetric probability limits as the distribution of the sample variability is not normal. Hence, the usual zone rules can not be applied although it is still desirable to be able to use the information from more than one point in decision making. In this paper, a modified S-chart based on an optimal normalizing transformation of the sample variance is first introduced. The new chart is shown to have approximate symmetric probability limits and hence can be interpreted in the same way as that of a ¯ X chart. This modified chart is shown to be comparable with the probability S-chart and have a much better performance than the usual Shewhart S-chart for the cases of known and estimated limits. The effect of parameter estimation is investigated. The optimal normalizing transformation is a simple power transformation. The power parameter depends only on the sample size and approaches 1/3 as the sample size increases. Hence, the transformation S-chart can be easily implemented and integrated into any SPC system. 2002-01-01T08:00:00Z text application/pdf https://ink.library.smu.edu.sg/soe_research/2064 https://ink.library.smu.edu.sg/context/soe_research/article/3063/viewcontent/YangXie2002.pdf http://creativecommons.org/licenses/by-nc-nd/4.0/ Research Collection School Of Economics eng Institutional Knowledge at Singapore Management University Econometrics
institution Singapore Management University
building SMU Libraries
continent Asia
country Singapore
Singapore
content_provider SMU Libraries
collection InK@SMU
language English
topic Econometrics
spellingShingle Econometrics
YANG, Zhenlin
Monitoring process variability with symmetric control limits
description Control charts for monitoring process variability, such as the R-chart and S-chart, do not have symmetric probability limits as the distribution of the sample variability is not normal. Hence, the usual zone rules can not be applied although it is still desirable to be able to use the information from more than one point in decision making. In this paper, a modified S-chart based on an optimal normalizing transformation of the sample variance is first introduced. The new chart is shown to have approximate symmetric probability limits and hence can be interpreted in the same way as that of a ¯ X chart. This modified chart is shown to be comparable with the probability S-chart and have a much better performance than the usual Shewhart S-chart for the cases of known and estimated limits. The effect of parameter estimation is investigated. The optimal normalizing transformation is a simple power transformation. The power parameter depends only on the sample size and approaches 1/3 as the sample size increases. Hence, the transformation S-chart can be easily implemented and integrated into any SPC system.
format text
author YANG, Zhenlin
author_facet YANG, Zhenlin
author_sort YANG, Zhenlin
title Monitoring process variability with symmetric control limits
title_short Monitoring process variability with symmetric control limits
title_full Monitoring process variability with symmetric control limits
title_fullStr Monitoring process variability with symmetric control limits
title_full_unstemmed Monitoring process variability with symmetric control limits
title_sort monitoring process variability with symmetric control limits
publisher Institutional Knowledge at Singapore Management University
publishDate 2002
url https://ink.library.smu.edu.sg/soe_research/2064
https://ink.library.smu.edu.sg/context/soe_research/article/3063/viewcontent/YangXie2002.pdf
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