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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.
Łukasz Smaga. "A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans." Biometrical Letters 53.2 (2016): 119-131. <http://eudml.org/doc/287153>.
@article{ŁukaszSmaga2016, 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.}, author = {Łukasz Smaga}, journal = {Biometrical Letters}, keywords = {blocked main effects plan; D-efficiency; D-optimality; Fischer’s inequality; Hadamard’s inequality; nonorthogonality}, language = {eng}, number = {2}, pages = {119-131}, title = {A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans}, url = {http://eudml.org/doc/287153}, volume = {53}, year = {2016}, }
TY - JOUR AU - Łukasz Smaga TI - A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans JO - Biometrical Letters PY - 2016 VL - 53 IS - 2 SP - 119 EP - 131 AB - 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. LA - eng KW - blocked main effects plan; D-efficiency; D-optimality; Fischer’s inequality; Hadamard’s inequality; nonorthogonality UR - http://eudml.org/doc/287153 ER -