Construction of asymmetrical orthogonal arrays having factors with a large non-prime power number of levels

Abstract

A general construction method is proposed for asymmetrical orthogonal arrays that have factors with a large number of levels and where that number is a non-prime power. In addition, the method's goal is to construct orthogonal arrays that are nearly saturated main-effect plans. The technique makes use of the method of replacement, in which a p 1-level factor and a p 2-level factor are replaced by a p 1 p 2-level factor. For q an odd prime power, the existence of orthogonal arrays with 4 q 2 runs and 2 q + 1 factors having 2 q and q levels is proved. This theorem produces many new orthogonal arrays. Other results include the construction of a new 72-run orthogonal array having factors with 12, 6, 3, and 2 levels that is more nearly saturated than other 72-run arrays, in the literature, that have more than one factor with 12 or 6 levels. New 144-run arrays are also constructed, such as one having seven factors with 12 levels and six factors with 2 levels and another array having factors with 12, 4, and 3 levels that is more nearly saturated than other known orthogonal arrays having more than two factors with 12 levels.