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ID:34374997
大小:186.68 KB
页数:12页
时间:2019-03-05
《invariance of generalized wordlength patternsnew》由会员上传分享,免费在线阅读,更多相关内容在教育资源-天天文库。
1、InvarianceofgeneralizedwordlengthpatternsJayH.BederJebF.WillenbringDepartmentofMathematicalSciencesUniversityofWisconsin-MilwaukeeP.O.Box413Milwaukee,WI53201-0413beder@uwm.edu,jw@uwm.eduAbstractThegeneralizedwordlengthpattern(GWLP)introducedbyXuandWu(2001)foranarbitraryfractionalfactoria
2、ldesignallowsonetoextendtheuseoftheminimumaber-rationcriteriontosuchdesigns.AiandZhang(2004)de¯nedtheJ-characteristicsofadesignandshowedthattheyuniquelydeterminethedesign.WhileboththeGWLPandtheJ-characteristicsrequireindexingthelevelsofeachfactorbyacyclicgroup,weseethatthede¯nitionscarry
3、overwithappropriatechangesifinsteadoneusesanarbitraryabeliangroup.Thismeansthattheoriginalde¯nitionsrestonanarbitrarychoiceofgroupstructure.WeshowthattheGWLPofadesignisindependentofthischoice,butthattheJ-characteristicsarenot.Webrie°ydiscusssomeimplicationsoftheseresults.Keywords.Fractio
4、nalfactorialdesign;groupcharacter;Hammingweight;multiset;orthogonalarrayAMS(MOS)subjectclassi¯cation.Primary:62K15;Secondary:05B15,15A69,20C15,62K051IntroductionInaregularfractionalfactorialdesignD,thequantitiesAi(D)=thenumberofde¯ningwordsoflengthicontainusefulinformationaboutthedesign.
5、Inparticular,thesmallestindexiforwhichAi(D)>0istheresolutionofthedesign.Moreover,onewayofcomparingtwodesignshavingkfactorsandequalresolutionistocomparetheirenterprisepatterns(A1;A2;:::;Ak)[5,6].Thebetterdesignissaidtohavelessaberration.Whilenonregulardesignsnolongerhavede¯ningwordsassuch
6、,ageneralizedwordlengthpattern(GWLP)canbede¯nedforthemcombinatorially.Thiswasdonefortwo-leveldesignsbyTangandDeng[12],andwasgeneralizedtoarbitrary(possiblymixed-level)designsbyXuandWu[14]usinggroupcharacters.Anintermediatecomputationinthetwo-levelcasegivesasetofvaluesthatTangandDengcalle
7、dJ-characteristics(¯rstintroducedin[4]),andTang[11]showedthatthesenumberscompletelydeterminethedesignD,somewhatanalogoustothewaythatade¯ningsubgroupdeterminesaregulardesign.AiandZhang[1]generalizedthistoarbitrarydesignsbylookingcloselyatthecorrespondingcomputationin[14].1
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