Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, ...Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.展开更多
This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will sho...This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.展开更多
The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration...The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.展开更多
基金the National Natural Science Foundation of China (No. 10771193)the Starter Foundation for the Doctors of Zhejiang Gongshang University(No. 1020XJ030517)+1 种基金the Natural Science Foundationof Universities of Jiangsu Province (No. 07KJB110090)the Starter Foundation for the Doctors of Nantong University (No. 07B12)
文摘Let （v, u × c,λ）-splitting BIBD denote a （v, u × c,λ）-splitting balanced incomplete block design of order v with block size u × c and index A. The necessary conditions for the existence of a （v, u × c,λ）-splitting BIBD are v ≥ uc, λ（v- 1） -- 0 0 mod （c（u- 1）） and Av（v- 1） - 0 mod （c^2u（u- 1））. In this paper, for 2 ≤λ≤ 9 the necessary conditions for the existence of a （v, 3 × 3, λ）-splitting BIBD are also sufficient with one possible exception for （v, λ） = （39, 9）.
基金National Natural Science Foundation ofChina(No.10 4710 93)
文摘This paper investigated the existence of splitting balanced incomplete block designs with blck size 2× k .The necessary conditions for such a design are λ(v-1) ≡0(mod k ),and λv(v- 1)≡0(mod 2 k 2).It will show that the above necessary conditions are also sufficient for k =3 with the definite exception( v,λ )=(10,1) and with several possible exceptions.
基金This work was partially supported by National Natural Science Foundation of China(Grant No.10231030)Chinese Postdoctoral Science Foundation(Grant No.20040350240).
文摘The issue of optimal blocking for fractional factorial split-plot (FFSP) designs is considered under the two criteria of minimum aberration and maximum estimation capacity. The criteria of minimum secondary aberration (MSA) and maximum secondary estimation capacity (MSEC) are developed for discriminating among rival nonisomorphic blcoked FFSP designs. A general rule for identifying MSA or MSEC blocked FFSP designs through their blocked consulting designs is established.
