<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper considers main effects plans used to study <italic>m</italic> two-level factors using <italic>n</italic> runs which are partitioned into <italic>b</italic> blocks of equal size <italic>k</italic> = <italic>n/b</italic>. The assumptions are adopted that <italic>n</italic> ≡ 2 (mod 8) and <italic>k</italic> > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by <xref ref-type="bibr" rid="j_bile-2016-0009_ref_010_w2aab2b8b6b1b7b1ab1ac10Aa">Jacroux (2011a)</xref> to be D-optimal when (<italic>m</italic> − 2)(<italic>k</italic> − 2) + 2 ⩽ <italic>n</italic> ⩽ (<italic>m</italic> − 1)(<italic>k</italic> − 2) + 2. Here, we extend that result. For (<italic>m</italic> − 3)(<italic>k</italic> − 2) + 2 ⩽ <italic>n</italic> &lt; (<italic>m</italic> − 2)(<italic>k</italic> − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(<italic>m</italic> + 1) ⩽ <italic>n</italic> &lt; (<italic>m</italic> − 3)(<italic>k</italic> − 2) + 2, indicating their good performance under the criterion of D-optimality.</p></abstract>

This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The assumptions are adopted that n ≡ 2 (mod 8) and k > 2 is even. Certain designs not having all main effects orthogonal to blocks were shown by Jacroux (2011a) to be D-optimal when (m − 2)(k − 2) + 2 ⩽ n ⩽ (m − 1)(k − 2) + 2. Here, we extend that result. For (m − 3)(k − 2) + 2 ⩽ n < (m − 2)(k − 2) + 2, the D-optimality of those designs is proved. Moreover, their D-efficiency is shown to be close to one for 2(m + 1) ⩽ n < (m − 3)(k − 2) + 2, indicating their good performance under the criterion of D-optimality.

A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań,

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper considers main effects plans used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. The...

A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

Published Online: Dec 10, 2016

Page range: 119 - 131

DOI: https://doi.org/10.1515/bile-2016-0009

Keywords
blocked main effects plan, D-efficiency, D-optimality, Fischer’s inequality, Hadamard’s inequality, nonorthogonality

© 2016 Łukasz Smaga, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans

Published Online: Dec 10, 2016

Page range: 119 - 131

DOI: https://doi.org/10.1515/bile-2016-0009

Keywordsblocked main effects plan, D-efficiency, D-optimality, Fischer’s inequality, Hadamard’s inequality, nonorthogonality

© 2016 Łukasz Smaga, published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
blocked main effects plan, D-efficiency, D-optimality, Fischer’s inequality, Hadamard’s inequality, nonorthogonality