Abstract
In this paper, we consider experimental situations where a main effects plan is to be used to study m two-level factors using n runs which are partitioned into b blocks of equal size k = n/b. It is shown that when \(n \equiv 2 \pmod{8}\) and k > 2, the best possible design under the D-optimality criterion does not necessarily have all factors orthogonal to blocks. In such situations, an alternative class of designs is suggested for usage which are better under the D-optimality criterion than the best available design having all main effects orthogonal to blocks.
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Jacroux, M. 2011. Optimal blocked main effect plans. Statistics (In Press).
Jacroux, M., Masaro, J. and Wong, C.S. 1983. On the optimality of chemical balance weighing designs. Journal of Statistical Planning and Inf. 8:231–240.
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Jacroux, M. On the D-optimality of nonorthogonal blocked main effects plans. Sankhya B 73, 62–69 (2011). https://doi.org/10.1007/s13571-011-0023-y
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DOI: https://doi.org/10.1007/s13571-011-0023-y