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Statistica Sinica 18(2008), 105-119





SECOND ORDER SATURATED ORTHOGONAL

ARRAYS OF STRENGTH THREE


Ching-Shui Cheng$^{1,2}$, Robert W. Mee$^3$ and Oksoun Yee$^4$


$^1$Academia Sinica, $^2$University of California, Berkeley,

$^3$University of Tennessee and $^4$Schering-Plough Corporation


Abstract: Strength three two-level orthogonal arrays with the number of runs $(N)$ equaling twice the number of factors $(k)$ are second-order saturated (SOS) designs. That is, for such designs one can construct a saturated model with an intercept, $k$ $(=N/2)$ main effects, and $N/2-1$ two-factor interactions. Projections of this design onto subsets of factors provide no more degrees of freedom for two-factor interactions. This article explores the construction of other second-order saturated strength three arrays that allocate more than $N/2$ degrees of freedom for two-factor interactions. These new orthogonal arrays are constructed using two methods, one based on a foldover technique that reverses the signs of a subset of the columns of the strength three orthogonal array with $k=N/2$, and the second based on the Kronecker product of an SOS design and a Hadamard matrix. We compare these new designs with respect to their generalized word length and alias length patterns.



Key words and phrases: Alias length pattern, complex aliasing, confounding frequency vector, doubling, foldover, nonregular design, resolution IV, two-factor interaction, word length pattern.

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