Some Results On Blocked Complementary Design Theory

The complementary design theory has received a great deal of attention in the recent literature. In particular, with some elementary material in coding theory including MacWilliams identities, Chen and Cheng (1999) developed a complementary design theory for blocked fractional factorials. In this paper, some new results for the blocked complementary design are reported, which extend the theory of Chen and Cheng (1999).On the other hand, in terms of run size flexibility and high estimation, non-regular fractional factorial designs have received much special notice. But there are very few literature on blocked non-regular complementary design theory. It is impossible to extend the theory and the method in Chen and Cheng (1999) to blocked non-regular ones. Using a set of J-characteristic values denned by Deng and Tang (1999), we define the generalized treatment-defining words, block-defining words and the relative words length. We also introduce a so-called eligible condition that the columns can be used for generating blocks. By studying ANOVA models, we develop a generalized blocked word length pattern criterion for blocked non-regular designs. Using this criterion, we give a natural extention of the blocked complementary design theory to non-regular ones.