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postgraduate thesis: Statistical process control charts with known and estimatedparameters

TitleStatistical process control charts with known and estimatedparameters
Authors
Advisors
Advisor(s):Yao, JJ
Issue Date2013
PublisherThe University of Hong Kong (Pokfulam, Hong Kong)
Citation
Yang, H. [阳华龙]. (2013). Statistical process control charts with known and estimated parameters. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5090001
AbstractMonitoring 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.
DegreeMaster of Philosophy
SubjectProcess control - Statistical methods.
Production management - Statistical methods.
Dept/ProgramStatistics and Actuarial Science
Persistent Identifierhttp://hdl.handle.net/10722/192856

 

DC FieldValueLanguage
dc.contributor.advisorYao, JJ-
dc.contributor.authorYang, Hualong-
dc.contributor.author阳华龙-
dc.date.accessioned2013-11-24T02:01:13Z-
dc.date.available2013-11-24T02:01:13Z-
dc.date.issued2013-
dc.identifier.citationYang, H. [阳华龙]. (2013). Statistical process control charts with known and estimated parameters. (Thesis). University of Hong Kong, Pokfulam, Hong Kong SAR. Retrieved from http://dx.doi.org/10.5353/th_b5090001-
dc.identifier.urihttp://hdl.handle.net/10722/192856-
dc.description.abstractMonitoring 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.-
dc.languageeng-
dc.publisherThe University of Hong Kong (Pokfulam, Hong Kong)-
dc.relation.ispartofHKU Theses Online (HKUTO)-
dc.rightsThe author retains all proprietary rights, (such as patent rights) and the right to use in future works.-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.source.urihttp://hub.hku.hk/bib/B50900018-
dc.subject.lcshProcess control - Statistical methods.-
dc.subject.lcshProduction management - Statistical methods.-
dc.titleStatistical process control charts with known and estimatedparameters-
dc.typePG_Thesis-
dc.identifier.hkulb5090001-
dc.description.thesisnameMaster of Philosophy-
dc.description.thesislevelMaster-
dc.description.thesisdisciplineStatistics and Actuarial Science-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.5353/th_b5090001-
dc.date.hkucongregation2013-

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