Optimal blocking and foldover plans for nonregular two-level designs |
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Authors: | Zujun Ou Hong Qin Hongyi Li |
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Affiliation: | a College of Mathematics and Computer Science, Jishou University, Jishou 416000, China b Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China c Normal College, Jishou University, Jishou 416000, China |
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Abstract: | This paper discusses the issue of choosing optimal designs when both blocking and foldover techniques are simultaneously employed to nonregular two-level fractional factorial designs. By using the indicator function, the treatment and block generalized wordlength patterns of the combined blocked design under a general foldover plan are defined. Some general properties of combined block designs are also obtained. Our results extend the findings of Ai et al. (2010) from regular designs to nonregular designs. Based on these theoretical results, a catalog of optimal blocking and foldover plans in terms of the generalized aberration criterion for nonregular initial design with 12, 16 and 20 runs is tabulated, respectively. |
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Keywords: | Combined blocked design Generalized minimum aberration Generalized resolution Indicator function |
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