{"id":"https://openalex.org/W937525589","doi":"https://doi.org/10.1198/004017007000000326","title":"Sample Size Determination for Achieving Stability of Double Multivariate Exponentially Weighted Moving Average Controller","display_name":"Sample Size Determination for Achieving Stability of Double Multivariate Exponentially Weighted Moving Average Controller","publication_year":2007,"publication_date":"2007-10-28","ids":{"openalex":"https://openalex.org/W937525589","doi":"https://doi.org/10.1198/004017007000000326","mag":"937525589"},"language":"en","primary_location":{"id":"doi:10.1198/004017007000000326","is_oa":false,"landing_page_url":"https://doi.org/10.1198/004017007000000326","pdf_url":null,"source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103130151","display_name":"Sheng\u2010Tsaing Tseng","orcid":"https://orcid.org/0000-0002-7050-6117"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Sheng-Tsaing Tseng","raw_affiliation_strings":["Institute of Statistics, National Tsing-Hua University, Hsin-Chu 30013, Taiwan, Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Statistics, National Tsing-Hua University, Hsin-Chu 30013, Taiwan, Republic of China","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040047709","display_name":"Jen Tang","orcid":"https://orcid.org/0000-0002-5960-148X"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jen Tang","raw_affiliation_strings":["Krannert Graduate School of Management, Purdue University, West Lafayette, IN 47907"],"affiliations":[{"raw_affiliation_string":"Krannert Graduate School of Management, Purdue University, West Lafayette, IN 47907","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100879283","display_name":"Chien-Hua Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chien-Hua Lin","raw_affiliation_strings":["Institute of Statistics, National Tsing-Hua University, Hsin-Chu 30013, Taiwan, Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Statistics, National Tsing-Hua University, Hsin-Chu 30013, Taiwan, Republic of China","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5103130151"],"corresponding_institution_ids":["https://openalex.org/I25846049"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05397161,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"49","issue":"4","first_page":"409","last_page":"419"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11443","display_name":"Advanced Statistical Process Monitoring","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11890","display_name":"Scientific Measurement and Uncertainty Evaluation","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11798","display_name":"Optimal Experimental Design Methods","score":0.9847999811172485,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mimo","display_name":"MIMO","score":0.7927646040916443},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.710913360118866},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.6260181069374084},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5937574505805969},{"id":"https://openalex.org/keywords/sample-size-determination","display_name":"Sample size determination","score":0.5251215100288391},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5089268684387207},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.48043227195739746},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.4555484354496002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4516085088253021},{"id":"https://openalex.org/keywords/process-control","display_name":"Process control","score":0.4102601110935211},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3263576030731201},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25629231333732605},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.16043514013290405},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10652497410774231},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.08318614959716797}],"concepts":[{"id":"https://openalex.org/C207987634","wikidata":"https://www.wikidata.org/wiki/Q176862","display_name":"MIMO","level":3,"score":0.7927646040916443},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.710913360118866},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.6260181069374084},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5937574505805969},{"id":"https://openalex.org/C129848803","wikidata":"https://www.wikidata.org/wiki/Q2564360","display_name":"Sample size determination","level":2,"score":0.5251215100288391},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5089268684387207},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.48043227195739746},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4555484354496002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4516085088253021},{"id":"https://openalex.org/C155386361","wikidata":"https://www.wikidata.org/wiki/Q1649571","display_name":"Process control","level":3,"score":0.4102601110935211},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3263576030731201},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25629231333732605},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.16043514013290405},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10652497410774231},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.08318614959716797},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C54197355","wikidata":"https://www.wikidata.org/wiki/Q5782992","display_name":"Beamforming","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1198/004017007000000326","is_oa":false,"landing_page_url":"https://doi.org/10.1198/004017007000000326","pdf_url":null,"source":{"id":"https://openalex.org/S985303","display_name":"Technometrics","issn_l":"0040-1706","issn":["0040-1706","1537-2723"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Technometrics","raw_type":"journal-article"},{"id":"mag:937525589","is_oa":false,"landing_page_url":"https://dialnet.unirioja.es/servlet/articulo?codigo=4617761","pdf_url":null,"source":{"id":"https://openalex.org/S13624874","display_name":"Quality Engineering","issn_l":"0898-2112","issn":["0898-2112","1532-4222"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Quality Engineering","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1549818157","https://openalex.org/W1782168110","https://openalex.org/W1968621901","https://openalex.org/W2063698478","https://openalex.org/W2065799639","https://openalex.org/W2084625130","https://openalex.org/W2104897439","https://openalex.org/W2133416631","https://openalex.org/W2149361748","https://openalex.org/W2170459004","https://openalex.org/W2170909262","https://openalex.org/W3125071194"],"related_works":["https://openalex.org/W2170459004","https://openalex.org/W2041971722","https://openalex.org/W9379550","https://openalex.org/W3175376631","https://openalex.org/W2095519829","https://openalex.org/W2049775470","https://openalex.org/W2580751104","https://openalex.org/W2765532952","https://openalex.org/W2847073989","https://openalex.org/W2323858577","https://openalex.org/W14413052","https://openalex.org/W2093544107","https://openalex.org/W3023123748","https://openalex.org/W2104917291","https://openalex.org/W1972990595","https://openalex.org/W3086112817","https://openalex.org/W2180359187","https://openalex.org/W2075247062","https://openalex.org/W1617614955","https://openalex.org/W2548026525"],"abstract_inverted_index":{"Many":[0],"semiconductor":[1],"manufacturing":[2],"processes":[3],"have":[4],"by":[5],"nature":[6],"multiple-input":[7],"and":[8,59,99,126,131],"multiple-output":[9],"(MIMO)":[10],"variables.":[11],"For":[12],"the":[13,21,38,61,106,123,128,132,135,146,149,157,161,169,176,191,200,212,230,239,242,249],"first-order":[14],"MIMO":[15,51,71,162,202,226],"process":[16,39,78,103,219],"with":[17,76,204],"a":[18,31,42,74,119,183,188,205,236],"linear":[19,136],"drift,":[20],"double":[22],"multivariate":[23],"exponentially":[24],"weighted":[25],"moving":[26],"average":[27],"(dMEWMA)":[28],"controller":[29,35,75],"is":[30,60,109,178,215],"popular":[32],"run-to-run":[33],"(R2R)":[34],"for":[36,160,190,199],"adjusting":[37],"mean":[40],"to":[41,97,196,217,228],"desired":[43],"target.":[44],"The":[45,67],"long-term":[46],"stability":[47,68,147,158,198],"of":[48,63,69,134,148,175,182,241,245],"this":[49,70,152],"closed-loop":[50,201],"system":[52,72,203],"has":[53],"not":[54],"yet":[55],"been":[56],"thoroughly":[57],"investigated":[58],"focus":[62],"our":[64],"present":[65],"study.":[66],"using":[73],"estimated":[77,170],"parameters":[79],"depends":[80],"on":[81,118,168,248],"whether":[82],"an":[83,113],"initial":[84],"input\u2013output":[85],"(I\u2013O)":[86],"predicted":[87,107],"model":[88,108],"can":[89],"be":[90],"obtained":[91],"successfully":[92],"in":[93,144,180],"advance":[94],"(i.e.,":[95],"offline)":[96],"accurately":[98],"precisely":[100],"estimate":[101],"these":[102,165],"parameters.":[104],"However,":[105],"typically":[110],"constructed":[111],"during":[112],"offline":[114,213],"DOE/RSM":[115,214],"stage,":[116],"based":[117],"random":[120],"sample":[121,129,193,251],"from":[122],"I\u2013O":[124,139,246],"variables,":[125],"thus":[127],"size":[130,194],"strength":[133],"relationship":[137],"between":[138],"variables":[140,247],"play":[141],"major":[142],"roles":[143],"determining":[145],"process.":[150,163],"In":[151],"article":[153],"we":[154,234],"first":[155],"obtain":[156,218],"conditions":[159,166,177],"Obviously,":[164],"depend":[167],"controller,":[171],"and,":[172],"consequently,":[173],"one":[174],"expressed":[179],"terms":[181],"probability.":[184,207],"We":[185,208,222],"then":[186],"derive":[187],"formula":[189],"adequate":[192],"required":[195,250],"achieve":[197],"guaranteed":[206],"also":[209],"describe":[210,235],"how":[211],"conducted":[216],"parameter":[220],"estimates.":[221],"give":[223],"two":[224],"practical":[225],"examples":[227],"illustrate":[229],"proposed":[231],"procedure.":[232],"Finally,":[233],"study":[237],"demonstrating":[238],"impact":[240],"covariance":[243],"structure":[244],"size.":[252]},"counts_by_year":[],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2025-10-10T00:00:00"}
