Control charts applying a sequential test at fixed sampling intervals with optional sampling at fixed times

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dc.contributor.authorStoumbos, Zachary G.en
dc.contributor.committeechairReynolds, Marion Jr.en
dc.contributor.committeememberArnold, Jesse C.en
dc.contributor.committeememberFoutz, Robert V.en
dc.contributor.committeememberHinkelmann, Klausen
dc.contributor.committeememberMyers, Raymonden
dc.contributor.committeememberYe, Keyingen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T21:16:04Zen
dc.date.adate2007-07-13en
dc.date.available2014-03-14T21:16:04Zen
dc.date.issued1993en
dc.date.rdate2007-07-13en
dc.date.sdate2007-07-13en
dc.description.abstractIn recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a sequential probability ratio test (SPRT) at fixed sampling intervals, the SPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the SPRT chart, the SPRT chart with sampling at fired times (SFT), is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. A third control chart is introduced as a generalization of the VSI cumulative sum (CUSUM) chart that uses two sampling intervals, called the universal CUSUM (UC) chart, in order to address the need for a general framework for the study of control charts that are equivalent to a sequence of SPRT’s. The UC chart can also be viewed as a generalization of the SPRT chart. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified with SFT versions of the SPRT chart, such as average time to signal (ATS), steady state ATS (SSATS), and average number of observations to signal (ANOS). After comparisons are performed within the general framework of the UC chart, the unmodified SPRT chart is found to be more efficient than both the FSI and VSI X charts and the FSI CUSUM chart, though very similar in efficiency to the VSI CUSUM chart. The modified SPRT chart with SFT is found to be more efficient than all five of the other control charts, including its unmodified version and the VSI CUSUM chart. General guidelines are provided for the design of both versions of the SPRT chart.en
dc.description.degreePh. D.en
dc.format.extentxviii, 248 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-07132007-143152en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-07132007-143152/en
dc.identifier.urihttp://hdl.handle.net/10919/38803en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1993.S868.pdfen
dc.relation.isformatofOCLC# 29895203en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1993.S868en
dc.subject.lcshQuality control -- Charts, diagrams, etcen
dc.titleControl charts applying a sequential test at fixed sampling intervals with optional sampling at fixed timesen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineStatisticsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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