Number representation method for obtaining two‐factor interaction columns in two‐level orthogonal arrays

In the Taguchi’s experimentations, orthogonal arrays, interaction tables, and linear graphs are provided for planning experiments, but they become quite unwieldy when the number of runs is large. The purpose of this article is to propose a quick and easy method for obtaining two‐factor interaction columns in two‐level orthogonal arrays. Geometrical designs proposed by Plackett and Burman are two‐level orthogonal arrays and can be obtained very easily by a successive doubling method. Based on the property of doubling, a NR method using a number representation system whose base is a power of 2 is derived in this article for obtaining two‐factor interaction columns in geometrical designs. Furthermore, since Taguchi’s two‐level orthogonal arrays are obtainable by successive doubling with some column permutations, it is shown that their two‐factor interaction columns can be obtained directly by using the NR method without looking up tables.