Statistica Sinica 22 (2012), 419-432

doi:http://dx.doi.org/10.5705/ss.2009.324

D-OPTIMAL PARTIALLY REPLICATED

TWO-LEVEL FACTORIAL DESIGNS

Shin-Fu Tsai$^1$, Chen-Tuo Liao$^1$ and Feng-Shun Chai$^2$

$^1$ National Taiwan University and $^2$ Academia Sinica

Abstract: When designing a two-level factorial experiment, a cost-effective compromise for obtaining a replication-based estimate of the error variance is to conduct a partial replication on unreplicated designs. In this article, based on the D-optimality criterion, we focus on selecting a partial replication from the orthogonal designs derived from Hadamard matrices. It is shown that the augmented designs, composed of the chosen partial replication and the orthogonal designs, are highly efficient. We obtain (i) sufficient conditions for the augmented designs to be D-optimal over their corresponding classes; (ii) a construction method for the desired designs.

Key words and phrases: Hadamard matrix, orthogonal array, projection property, pure error.