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dc.contributor.authorXu, Liaosaen_US
dc.date.accessioned2014-08-22T06:00:08Z
dc.date.available2014-08-22T06:00:08Z
dc.date.issued2013-02-27en_US
dc.identifier.othervt_gsexam:352en_US
dc.identifier.urihttp://hdl.handle.net/10919/50408
dc.description.abstractGeneralized likelihood ratio (GLR) control charts are investigated for two types of statistical process monitoring (SPC) problems.

The first part of this dissertation considers the problem of monitoring a normally distributed process variable when a special cause may produce a time varying linear drift in the mean. The design and application of a GLR control chart for drift detection is investigated. The GLR drift chart does not require specification of any tuning parameters by the practitioner, and has the advantage that, at the time of the signal, estimates of both the change point and the drift rate are immediately available. An equation is provided to accurately approximate the control limit. The performance of the GLR drift chart is compared to other control charts such as a standard CUSUM chart and a CUSCORE chart designed for drift detection. We also compare the GLR chart designed for drift detection to the GLR chart designed for sustained shift detection since both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change-point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out-of-control process is truly a linear drift.

The second part of the dissertation considers the problem of monitoring a linear functional relationship between a response variable and one or more explanatory variables (a linear profile). The design and application of GLR control charts for this problem are investigated. The likelihood ratio test of the GLR chart is generalized over the regression coefficients, the variance of the error term, and the possible change-point. The performance of the GLR chart is compared to various existing control charts. We show that the overall performance of the GLR chart is much better than other options in detecting a wide range of shift sizes. The existing control charts designed for certain shifts that may be of particular interest have several chart parameters that need to be specified by the user, which makes the design of such control charts more difficult. The GLR chart is very simple to design, as it is invariant to the choice of design matrix and the values of in-control parameters. Therefore there is only one design parameter (the control limit) that needs to be specified. Especially, the GLR chart can be constructed based on the sample size of n=1 at each sampling point, whereas other charts cannot be applied. Another advantage of the GLR chart is its built-in diagnostic aids that provide estimates of both the change-point and the values of linear profile parameters.
en_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis Item is protected by copyright and/or related rights. Some uses of this Item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectAbrupt Changeen_US
dc.subjectAverage Time to Signalen_US
dc.subjectChange Pointen_US
dc.subjectCUSUM Charten_US
dc.subjectEWMA Charten_US
dc.subjectGeneralized Likelihood Ratioen_US
dc.subjectLinear Regressionen_US
dc.subjectIen_US
dc.titleThe Design of GLR Control Charts for Process Monitoringen_US
dc.typeDissertationen_US
dc.contributor.departmentStatisticsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineStatisticsen_US
dc.contributor.committeechairReynolds, Marion R. Jr.en_US
dc.contributor.committeememberHong, Yilien_US
dc.contributor.committeememberKim, Dong-Yun Hanen_US
dc.contributor.committeememberWoodall, William H.en_US


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