Mukerjee and Wu（2001） employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In ...Mukerjee and Wu（2001） employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level （2^r）2^n factorial design to that of its consulting design. Consequently, a general rule for identifying minimum aberration （2^r）2^n factorial designs through their consulting designs is established. It is an improvement and generalization of the related result in Mukerjee and Wu（2001）.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
文摘Mukerjee and Wu（2001） employed projective geometry theory to find the wordlength pattern of a regular mixed factorial design in terms of its complementary set, but only for the numbers of words of length 3 or 4. In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain some combinatorial identities that relate the wordlength pattern of a regular mixed-level （2^r）2^n factorial design to that of its consulting design. Consequently, a general rule for identifying minimum aberration （2^r）2^n factorial designs through their consulting designs is established. It is an improvement and generalization of the related result in Mukerjee and Wu（2001）.
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.
