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TIGHT ASYMMETRIC ORTHOGONAL ARRAYS OF STRENGTH 2 USING FINITE PROJECTIVE GEOMETRY
Aggarwal M.L.,Deng Lih Yuan,Mazumder Mukta D. The Korean Statistical Society 2006 Journal of the Korean Statistical Society Vol.35 No.1
Wu et al. (1992) constructed some general classes of tight asymmetric orthogonal arrays of strength 2 using the method of grouping. Rains et al. (2002) obtained asymmetric orthogonal arrays of strength 2 using the concept of mixed spread in finite projective geometry. In this paper, we obtain some new tight asymmetric orthogonal arrays of strength 2 using the concept of mixed partition in finite projective geometry.
TIGHT ASYMMETRIC ORTHOGONAL ARRAYS OF STRENGTH 2 USING FINITE PROJECTIVE GEOMETRY
M. L. AGGARWAL,LIH-YUAN DENG,MUKTA D. AZUMDER 한국통계학회 2006 Journal of the Korean Statistical Society Vol.35 No.1
Wu et al:(1992) constructed some general classes of tight asymmetricet al:(2002) obtained asymmetric orthogonal arrays of strength 2 using the con-cept of mixed spread in nite projective geometry. In this paper, we obtainsome new tight asymmetric orthogonal arrays of strength 2 using the conceptof mixed partition in nite projective geometry.AMS 2000 subject classications.Primary 62K15; Secondary 05B15.Keywords.Tight asymmetric orthogonal array, mixed spread, mixed partition, ats.1. IntroductionRao (1973) introduced asymmetric orthogonal arrays which have found nu-merous applications for quality improvements in the context of the industrialexperiments as pointed out by Taguchi (1987). An asymmetric orthogonal ar-ray OA(N;k;mk11 mk22 mknn ;t N k where k =k1 + k2 + + kn is the total number of factors in whichk1 columns have m1symbols ranging fromf0;1;:;m 1 1g, the nextk2 columns have m2 sym-bols ranging fromf0;1;:;m 2 1g and so on with the property that in anyN t subarray every possiblet row. An OA(N;k;mk11 mk22 mknn ;2) attaining Rao's boundN 1 +k1(m1 1) + k2(m2 1) + + kn(mn 1) is called tight. The special casem1 = m2 = = mn = m, (say) corresponds to a symmetric orthogonal array,denoted by an OA( ).Received August 2004; accepted February 2006.1Corresponding author. Department of Mathematical Sciences, The University of Memphis,Memphis, TN 38152, USA (e-mail : maggarwl@memphis.edu)