Choice of optimal initial designs in sequential experiments

Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking factor. In this paper, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new class of designs is called blocked combined-optimal designs. Some general results are obtained which relate 2<Superscript> k </Superscript> <Superscript>−</Superscript> <Superscript> p </Superscript> <Subscript>III</Subscript> initial designs with their complementary designs when [InlineMediaObject not available: see fulltext.], where n=2<Superscript> k </Superscript> <Superscript>−</Superscript> <Superscript> p </Superscript>. By applying these results, we are able to characterize 2<Superscript> k </Superscript> <Superscript>−</Superscript> <Superscript> p </Superscript> <Subscript>III</Subscript> combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that both 2<Superscript> k </Superscript> <Superscript>−</Superscript> <Superscript> p </Superscript> <Subscript>III</Subscript> combined-optimal and blocked combined-optimal designs are not minimum aberration designs when [InlineMediaObject not available: see fulltext.] and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration. Copyright Springer-Verlag 2005