Statistical process control charts with known and estimatedparameters
Monitoring and detection of abrupt changes for multivariate processes are becoming increasingly important in modern manufacturing environments. Typical equipment may have multiple key variables to be measured continuously. Hotelling's 〖T 〗^2and CUSUM charts were widely applied to solve the pro...
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The University of Hong Kong (Pokfulam, Hong Kong)
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ndltd-HKU-oai-hub.hku.hk-10722-1928562015-07-29T04:02:17Z Statistical process control charts with known and estimatedparameters Yang, Hualong 阳华龙 Yao, JJ Process control - Statistical methods. Production management - Statistical methods. Monitoring and detection of abrupt changes for multivariate processes are becoming increasingly important in modern manufacturing environments. Typical equipment may have multiple key variables to be measured continuously. Hotelling's 〖T 〗^2and CUSUM charts were widely applied to solve the problem of monitoring the mean vector of multivariate quality measurements. Besides, a new multivariate cumulative sum chart (MCUSUM) is introduced where the target shift mean is assumed to be a weighted sum of principal directions of the population covariance matrix. In practical problems, estimated parameters are needed and the properties of control charts differ from the case where the parameters are known in advance. In particular, it has been observed that the average run length (ARL), a performance indicator of the control charts, is larger when the estimated parameters are used. As a first contribution we provide a general and formal proof of the phenomenon. Also, to design an efficient 〖T 〗^2 or CUSUM chart with estimated parameters, a method to calculate or approximate the ARL function is necessarily needed. A commonly used approach consists in tabulating reference values using extensive Monte-Carlo simulation. By a different approach in thesis, an analytical approximation for the ARL function in univariate case is provided, especially in-control ARL function, which can help to directly set up control limits for different sample sizes of Phase I procedure instead of conducting complex simulation. published_or_final_version Statistics and Actuarial Science Master Master of Philosophy 2013-11-24T02:01:13Z 2013-11-24T02:01:13Z 2013 2013 PG_Thesis 10.5353/th_b5090001 b5090001 http://hdl.handle.net/10722/192856 eng HKU Theses Online (HKUTO) The author retains all proprietary rights, (such as patent rights) and the right to use in future works. Creative Commons: Attribution 3.0 Hong Kong License The University of Hong Kong (Pokfulam, Hong Kong) http://hub.hku.hk/bib/B50900018 |
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English |
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Process control - Statistical methods. Production management - Statistical methods. |
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Process control - Statistical methods. Production management - Statistical methods. Yang, Hualong 阳华龙 Statistical process control charts with known and estimatedparameters |
description |
Monitoring and detection of abrupt changes for multivariate processes are becoming increasingly important in modern manufacturing environments. Typical equipment may have multiple key variables to be measured continuously. Hotelling's 〖T 〗^2and CUSUM charts were widely applied to solve the problem of monitoring the mean vector of multivariate quality measurements. Besides, a new multivariate cumulative sum chart (MCUSUM) is introduced where the target shift mean is assumed to be a weighted sum of principal directions of the population covariance matrix. In practical problems, estimated parameters are needed and the properties of control charts differ from the case where the parameters are known in advance. In particular, it has been observed that the average run length (ARL), a performance indicator of the control charts, is larger when the estimated parameters are used. As a first contribution we provide a general and formal proof of the phenomenon. Also, to design an efficient 〖T 〗^2 or CUSUM chart with estimated parameters, a method to calculate or approximate the ARL function is necessarily needed. A commonly used approach consists in tabulating reference values using extensive Monte-Carlo simulation. By a different approach in thesis, an analytical approximation for the ARL function in univariate case is provided, especially in-control ARL function, which can help to directly set up control limits for different sample sizes of Phase I procedure instead of conducting complex simulation. === published_or_final_version === Statistics and Actuarial Science === Master === Master of Philosophy |
author2 |
Yao, JJ |
author_facet |
Yao, JJ Yang, Hualong 阳华龙 |
author |
Yang, Hualong 阳华龙 |
author_sort |
Yang, Hualong |
title |
Statistical process control charts with known and estimatedparameters |
title_short |
Statistical process control charts with known and estimatedparameters |
title_full |
Statistical process control charts with known and estimatedparameters |
title_fullStr |
Statistical process control charts with known and estimatedparameters |
title_full_unstemmed |
Statistical process control charts with known and estimatedparameters |
title_sort |
statistical process control charts with known and estimatedparameters |
publisher |
The University of Hong Kong (Pokfulam, Hong Kong) |
publishDate |
2013 |
url |
http://hdl.handle.net/10722/192856 |
work_keys_str_mv |
AT yanghualong statisticalprocesscontrolchartswithknownandestimatedparameters AT yánghuálóng statisticalprocesscontrolchartswithknownandestimatedparameters |
_version_ |
1716813893966233600 |