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

摘要

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 quickand 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 theproperty 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 areobtainable 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.