Economically optimum design of cusum charts when there is a multiplicity of assignable causes

dc.contributor.authorHsu, Margaretha Mei-Ingen
dc.contributor.committeechairReynolds, Marion R. Jr.en
dc.contributor.committeememberHinkelmann, Klaus H.en
dc.contributor.committeememberKramer, Clyde Y.en
dc.contributor.committeememberMyers, Raymond H.en
dc.contributor.committeememberSchmidt, J. Williamen
dc.contributor.departmentStatisticsen
dc.date.accessioned2014-03-14T21:10:00Zen
dc.date.adate2010-03-02en
dc.date.available2014-03-14T21:10:00Zen
dc.date.issued1978-10-05en
dc.date.rdate2010-03-02en
dc.date.sdate2010-03-02en
dc.description.abstractThis study is concerned with the design of cumulative sum charts based on a minimum cost criterion when there are multiple assignable causes occurring randomly, but with known effect. A cost model is developed that relates the design parameters (i.e. sampling interval, decision limit, reference value and sample size) of a cusum chart and the cost and risk factors of the process to the long run average loss cost per hour for the process. Optimum designs for various sets of cost and risk factors are found by minimizing the long run average loss-cost per hour of the process with respect to the design parameters of a cusum chart. Optimization is accomplished by use of Brown's method. A modified Brownian motion approximation is used for calculating ARLs in the cost model. The nature of the loss-cost function is investigated numerically. The effects of changes in the design parameters and in the cost and risk factors are also studied. An investigation of the limiting behavior of the loss-cost function as the decision limit approaches infinity reveals that in some cases there exist some points that yield a lower loss-cost than that of the local minimum obtained by Brown's method. It is conjectured that if the model is extended to include more realistic assumption about the occurrence of assignable causes then only the local minimum solutions will remain. This paper also shows that the multiple assignable cause model can be well approximated by a matched single cause model. Then in practice it may be sufficient to find the optimum design for the matched. single cause model.en
dc.description.degreePh. D.en
dc.format.extentvii, 81 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-03022010-020326en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-03022010-020326/en
dc.identifier.urihttp://hdl.handle.net/10919/37473en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1978.H88.pdfen
dc.relation.isformatofOCLC# 40294097en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectcost modelsen
dc.subjectcumulative sum chartsen
dc.subject.lccLD5655.V856 1978.H88en
dc.titleEconomically optimum design of cusum charts when there is a multiplicity of assignable causesen
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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