Show simple item record

dc.contributor.authorWilson, Sara R.en_US
dc.date.accessioned2014-03-14T21:10:30Z
dc.date.available2014-03-14T21:10:30Z
dc.date.issued2009-04-03en_US
dc.identifier.otheretd-04142009-133018en_US
dc.identifier.urihttp://hdl.handle.net/10919/37623
dc.description.abstractTraditional control charts for process monitoring are based on taking samples from the process at regular time intervals. However, it is often possible in practice for observations, and even entire samples, to be missing. This dissertation investigates missing observations in Exponentially Weighted Moving Average (EWMA) and Multivariate EWMA (MEWMA) control charts. The standardized sample mean is used since this adjusts the sample mean for the fact that part of the sample may be missing. It also allows for constant control limits even though the sample size varies randomly. When complete samples are missing, the weights between samples should also be adjusted. In the univariate case, three approaches for adjusting the weights of the EWMA control statistic are investigated: (1) ignoring missing samples; (2) adding the weights from previous consecutive missing samples to the current sample; and (3) increasing the weights of non-missing samples in proportion, so that the weights sum to one. Integral equation and Markov chain methods are developed to find and compare the statistical properties of these charts. The EI chart, which adjusts the weights by ignoring the missing samples, has the best overall performance. The multivariate case in which information on some of the variables is missing is also examined using MEWMA charts. Two methods for adjusting the weights of the MEWMA control statistic are investigated and compared using simulation: (1) ignoring all the data at a sampling point if the data for at least one variable is missing; and (2) using the previous EWMA value for any variable for which all the data are missing. Both of these methods are examined when the in-control covariance matrix is adjusted at each sampling point to account for missing observations, and when it is not adjusted. The MS control chart, which uses the previous value of the EWMA statistic for a variable if all of the data for that variable is missing at a sampling point, provides the best overall performance. The in-control covariance matrix needs to be adjusted at each sampling point, unless the variables are independent or only weakly correlated.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartSRW-ETD.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectATSen_US
dc.subjectStatistical process controlen_US
dc.subjectcontrol charten_US
dc.subjectEWMAen_US
dc.subjectMEWMAen_US
dc.titleControl Charts with Missing Observationsen_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.committeememberKim, Dong-Yunen_US
dc.contributor.committeememberSmith, Eric P.en_US
dc.contributor.committeememberWoodall, William H.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04142009-133018/en_US
dc.date.sdate2009-04-14en_US
dc.date.rdate2009-05-05
dc.date.adate2009-05-05en_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record