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Volume (53) Number 2 pp. 119-131
Łukasz Smaga 1
1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614Poznań, Poland
A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans
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 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.
Keywords: blocked main effects plan, D-efficiency, D-optimality, Fischer’s inequality, Hadamard’s inequality, nonorthogonality
DOI: 10.1515/bile-2016-0009
For citation:
| MLA | Smaga, Łukasz. "A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans." Biometrical Letters 53.2 (2016): 119-131. DOI: 10.1515/bile-2016-0009 |
| APA | Smaga, . (2016). A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans. Biometrical Letters 53(2), 119-131 DOI: 10.1515/bile-2016-0009 |
| ISO 690 | SMAGA, Łukasz. A note on the D-optimality and D-efficiency of nonorthogonal blocked main effects plans. Biometrical Letters, 2016, 53.2: 119-131. DOI: 10.1515/bile-2016-0009 |