A unified approach in addition or deletion of two level factorial designs
✍ Scribed by H. Evangelaras; C. Koukouvinos; P. Mantas
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 118 KB
- Volume
- 59
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
✦ Synopsis
Suppose it is desired to have an optimal resolution III fraction of a 2 p factorial in n runs where n ≡ 1 (mod 4) or n ≡ 3 (mod 4). If n ≡ 1 (mod 4), we have to decide if we should add a run in a n × p submatrix of a Hadamard matrix of order n, say H n or, alternatively, if we should delete three runs from a (n + 4) × p submatrix of a Hadamard matrix of order n + 4, say H n+4 , in an optimal manner, respectively. Similarly, when n ≡ 3 (mod 4), we have to decide between optimally adding three more runs to a n × p submatrix of H n or optimally deleting a single run from a (n + 4) × p submatrix of H n+4 . The question to be studied is whether both strategies give designs that are equally e cient in terms of a well deÿned optimality criterion.
We show that, in both cases, for p = 3 both strategies give equally e cient designs under the D-or the A-optimality criterion. When n ≡ 1 (mod 4) and p ¿ 3, both criteria show that the "addition" design is always better than the "deletion" design. However, when n ≡ 3 (mod 4) and p ¿ 3, the choice of the most e cient design varies as p enlarges.