Statistica Sinica 23 (2013), 853-872

MINIMUM ABERRATION DESIGNS FOR

TWO-LEVEL FACTORIALS IN $\bm{N =}$ 1 (MOD 4) RUNS

Runchu Zhang$^{1,2,3}$ and Rahul Mukerjee$^4$

$^1$Northeast Normal University, $^2$The University of British Columbia,

$^3$Nankai University and $^4$Indian Institute of Management Calcutta

Abstract: Two-level minimum aberration (MA) designs in $N = 1$ (mod 4) runs are studied. For this purpose, we consider designs obtained by adding any single run to a two-symbol orthogonal array (OA) of strength two and then, among these designs, sequentially minimize a measure of bias due to interactions of successively higher orders. The reason for considering such OA plus one run designs is that they are optimal main effect plans in a very broad sense in the absence of interactions. Our approach aims at ensuring model robustness even when interactions are possibly present. It is shown that the MA criterion developed here has an equivalent formulation which is similar but not identical to the minimum moment aberration criterion. This formulation is utilized to derive theoretical results on and construct tables of MA designs in the present context.

Key words and phrases: Augmentation, bias, effect hierarchy, effect sparsity, Hadamard matrix, interaction, main effect, minimum moment aberration, nonorthogonality, orthogonal array.