Abstract
The concept of minimum aberration (MA) is a well-accepted criterion for selecting good fractional factorial designs, in both unblocked and blocked designs with a single block variable. This paper extends the concept to blocked designs with multiple block variables and considers the construction of MA blocked designs with multiple block variables with respect to two wordlength patterns. By using a finite projective geometric approach, we obtain identities that govern the relationship between the blocking wordlength patterns of a general blocked design and a relatively small blocked design with the same block factors. Based on these identities, we establish the rules for finding MA designs with multiple block variables in terms of the relatively small blocked designs. Some MA blocked designs are tabulated.
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Acknowledgements
The authors would like to thank the associate editor and two reviewers for their constructive comments and suggestions. This work was supported by National Natural Science Foundation of China (Grant Nos. 11771250, 11801308), Natural Science Foundation of Shandong Province (Grant No. ZR2018BA013), A Project of Shandong Province Higher Educational Science and Technology Program (No. J18KA246), and the Scientific and Technological Program of Qufu Normal University (No. xkj201519).
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Appendix: Tables
Appendix: Tables
See Tables 2, 3, 4, 5, 6, and 7.
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Zhao, S., Zhao, Q. Minimum aberration blocked designs with multiple block variables. Metrika 84, 121–140 (2021). https://doi.org/10.1007/s00184-020-00761-7
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DOI: https://doi.org/10.1007/s00184-020-00761-7