Abstract
As a generalization of alias balanced designs due to Hedayat, Raktoe and Federer [5], we introduce the concept of alias partially balanced designs for fractional 2m factorial designs of resolution 2l+1. All orthogonal arrays of strength 2l yield alias balanced designs. Some balanced arrays of strength 2l yield alias balanced and alias partially balanced designs. In particular, simple arrays which are a special case of balanced arrays yield alias partially balanced designs. At most 2m−1 alias balanced (or alias partially balanced) designs are generated from an alias balanced (or alias partially balanced) design by level permutations. This implies that alias balanced or alias partially balanced designs need not be orthogonal arrays or balanced arrays of strength 2l.
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Shirakura, T. Alias balanced and alias partially balanced fractional 2m factorial designs of resolution 2l+1. Ann Inst Stat Math 31, 57–65 (1979). https://doi.org/10.1007/BF02480265
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DOI: https://doi.org/10.1007/BF02480265