{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/42422"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/42422","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The application of a single control chart for dependent variables in multivariate quality control","abstract":"Most control charts monitor only one quality characteristic. There are, however, many manufactured products for which good quality requires meeting specifications in more than one physical characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate sample for each characteristic and then create individual univariate control charts which are independently monitored. This method can result in errors due to not accounting for the effects of correlation. In order to avoid these errors, an alternate approach to multivariate quality control problems is proposed and studied here. The original problem is converted into a univariate problem by using the following transformation: y=Σ a<sub>i</sub>x<sub>i</sub> i where αi = weighting coefficient for the i<sup>th</sup> quality characteristic X<sub>i</sub> = represents the i<sup>th</sup> quality characteristic This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs.","abstract_html":"Most control charts monitor only one quality characteristic. There are, however, many manufactured products for which good quality requires meeting specifications in more than one physical characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate sample for each characteristic and then create individual univariate control charts which are independently monitored. This method can result in errors due to not accounting for the effects of correlation. In order to avoid these errors, an alternate approach to multivariate quality control problems is proposed and studied here. The original problem is converted into a univariate problem by using the following transformation: y=Σ a&lt;sub&gt;i&lt;/sub&gt;x&lt;sub&gt;i&lt;/sub&gt; i where αi = weighting coefficient for the i&lt;sup&gt;th&lt;/sup&gt; quality characteristic X&lt;sub&gt;i&lt;/sub&gt; = represents the i&lt;sup&gt;th&lt;/sup&gt; quality characteristic This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs.","abstract_has_math":false,"creators":["Hanson, Robert Alexander"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Industrial Engineering and Operations Research","degree_department":"Industrial Engineering and Operations Research","school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":["Nachlas, Joel A.","Schmidt, J. William","Fabrycky, Wolter J."],"year":1990,"date_issued":"1990-08-05","date_published":"1990-08-05","updated_at":"2026-07-22T22:20:43Z","subjects":[],"languages":["en"],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05022009-040726"],"render_values":[{"text":"etd-05022009-040726","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/42422","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Nachlas, Joel A.","Schmidt, J. William","Fabrycky, Wolter J."]},{"key":"dc:contributor.department","label":"Department","values":["Industrial Engineering and Operations Research"]},{"key":"dc:creator","label":"Author","values":["Hanson, Robert Alexander"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T21:35:23Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T21:35:23Z","2009-05-02"]},{"key":"dc:date.issued","label":"Date","values":["1990-08-05"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.dcmitype","label":"Dc Type Dcmitype","values":["Text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Industrial Engineering and Operations Research"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-05022009-040726"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/42422"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Most control charts monitor only one quality characteristic. There are, however, many manufactured products for which good quality requires meeting specifications in more than one physical characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate sample for each characteristic and then create individual univariate control charts which are independently monitored. This method can result in errors due to not accounting for the effects of correlation. In order to avoid these errors, an alternate approach to multivariate quality control problems is proposed and studied here. The original problem is converted into a univariate problem by using the following transformation: y=Σ a<sub>i</sub>x<sub>i</sub> i where αi = weighting coefficient for the i<sup>th</sup> quality characteristic X<sub>i</sub> = represents the i<sup>th</sup> quality characteristic This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["BTD"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The application of a single control chart for dependent variables in multivariate quality control"]}]}],"canonical_facts":{"dc:contributor.committeemember":["Nachlas, Joel A.","Schmidt, J. William","Fabrycky, Wolter J."],"dc:contributor.department":["Industrial Engineering and Operations Research"],"dc:creator":["Hanson, Robert Alexander"],"dc:date.accessioned":["2014-03-14T21:35:23Z"],"dc:date.available":["2014-03-14T21:35:23Z","2009-05-02"],"dc:date.issued":["1990-08-05"],"dc:description.abstract":["Most control charts monitor only one quality characteristic. There are, however, many manufactured products for which good quality requires meeting specifications in more than one physical characteristic. Typical practice when dealing with multiple quality characteristics is to take a separate sample for each characteristic and then create individual univariate control charts which are independently monitored. This method can result in errors due to not accounting for the effects of correlation. In order to avoid these errors, an alternate approach to multivariate quality control problems is proposed and studied here. The original problem is converted into a univariate problem by using the following transformation: y=Σ a<sub>i</sub>x<sub>i</sub> i where αi = weighting coefficient for the i<sup>th</sup> quality characteristic X<sub>i</sub> = represents the i<sup>th</sup> quality characteristic This transformation retains sensitivity to changes in the original quality variables. The resulting univariate quality control model takes into account the sampling error probabilities for each of several candidate hypotheses. The probabilities of correctly diagnosing process shifts when an out-of-control state occurs are calculated and tabulated as are the probabilities that the model will signal when an out-of-control state occurs."],"dc:description.degree":["Master of Science"],"dc:format.medium":["BTD"],"dc:format.mimetype":["application/pdf"],"dc:identifier.other":["etd-05022009-040726"],"dc:identifier.uri":["http://hdl.handle.net/10919/42422"],"dc:language.iso":["en"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:title":["The application of a single control chart for dependent variables in multivariate quality control"],"dc:type":["Thesis"],"dc:type.dcmitype":["Text"],"thesis:degree_discipline":["Industrial Engineering and Operations Research"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:43Z"}