Basic Quaternary Design Table Using Geometrical Design

Purpose Taguchi provided some useful tools such as various orthogonal arrays, interaction tables, linear graphs, etc. for planning fractional factorial experiments and had many successful application cases in quality engineering (Taguchi, 1986). However, many research articles explored the methods that were used to construct those tools and tried to improve them. The aim of this article is to develop a new tool to substitute the uses of Taguchi’s orthogonal arrays and interaction tables. Design/methodology/approach Using a number representation system whose base is a power of 2, Tsai (1999) developed an easy algorithm for obtaining multi-factor interaction columns in geometrical designs, which serves as theoretic background for the development of a new tool. Finding Based on the algorithm of base 4, in this article we propose a Basic Quaternary Design Table (BQDT) which is a 4 by 4 squared matrix with entries of both decimal and quaternary column numbers. A BQDT has a nice structure of confounding relationships so that users could identify multi-factor interaction columns in a straightforward manner without looking up tables. The advantages of the proposed BQDT include (1) it serves as an efficient tool for column assignment problem; (2) it can substitute the use of Taguchi’s interaction table; (3) it is visually appealing such that the users can easily recognize some special designs. Originality/value Both geometrical design matrix and the BQDT can be used jointly to plan a two-level fractional factorial experiment without looking up tables, which can substitute the uses of Taguchi’s orthogonal arrays and interaction tables when run size n is a power of 2.