Projection properties of some orthogonal arrays

In factor screening experiments, one generally starts with a large pool of potentially important factors. However, often only a few of these are really active. Under this assumption of effect sparsity, while choosing a design for factor screening, it is important to consider projections of the design on to smaller subsets of factors and examine whether the projected designs allow estimability of some interactions along with the main effects. While the projectivity properties of symmetric 2-level and a few 3-level fractional factorial designs represented by orthogonal arrays have been studied in the literature, similar studies in respect of asymmetric or, mixed level factorials seems to be lacking. In this paper, we initiate work in this direction by providing designs with good projectivity properties for asymmetric factorials of the type tx2m based on orthogonal arrays. We also note that the results of Cheng (1995) regarding the projectivity of symmetric two-symbol orthogonal arrays do not necessarily extend to arrays with more than two symbols.