Construction of blocked designs with multi block variables

Yuna Zhao; Yuna Zhao

doi:10.3934/math.2021369

AIMS Mathematics

2021, Volume 6, Issue 6: 6293-6308. doi: 10.3934/math.2021369

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Research article

Construction of blocked designs with multi block variables

Yuna Zhao ^,

School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Received: 03 February 2021 Accepted: 25 March 2021 Published: 09 April 2021
MSC : 62K05, 62K15

When experimental units are inhomogeneous, blocking the experimental units into categories is crucial so as to estimate the treatment effects precisely. In practice, the inhomogeneity often comes from different sources known as block variables in design terminology. The paper considers the blocking problems with multi block variables. The construction methods of the optimal blocked regular $ 2^{n-m} $ designs with multi block variables under the general minimum lower order confounding criterion for $ \frac{5N}{16}+1\leq n \leq N-1 $ are provided, where $ N = 2^{n-m} $.
- blocked design,
- factional factorial design,
- general minimum lower order confounding,
- multi block variables,
- optimality
Citation: Yuna Zhao. Construction of blocked designs with multi block variables[J]. AIMS Mathematics, 2021, 6(6): 6293-6308. doi: 10.3934/math.2021369

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Abstract

When experimental units are inhomogeneous, blocking the experimental units into categories is crucial so as to estimate the treatment effects precisely. In practice, the inhomogeneity often comes from different sources known as block variables in design terminology. The paper considers the blocking problems with multi block variables. The construction methods of the optimal blocked regular $ 2^{n-m} $ designs with multi block variables under the general minimum lower order confounding criterion for $ \frac{5N}{16}+1\leq n \leq N-1 $ are provided, where $ N = 2^{n-m} $.

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