Choice of optimal initial designs in sequential experiments |
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Authors: | Peng-Fei Li Min-Qian Liu Run-Chu Zhang |
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Affiliation: | (1) Department of Statistics, School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China |
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Abstract: | 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 2k−pIII initial designs with their complementary designs when , where n=2k−p. By applying these results, we are able to characterize 2k−pIII combined-optimal designs or blocked combined-optimal designs in terms of their complementary designs. It is also proved that both 2k−pIII combined-optimal and blocked combined-optimal designs are not minimum aberration designs when and n−1−k > 2. And some combined-optimal and blocked combined-optimal designs with 16 and 32 runs are constructed for illustration. 2000 Mathematics Subject Classifications: 62K15, 62K05 |
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Keywords: | Combined design combined-optimal design complementary design foldover minimum aberration wordlength pattern |
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