Taguchi's Fixed-Element Arrays are Fractional Factorials

Taguchi developed his catalog of orthogonal arrays from mathematical procedures published in well-known English language journals. These arrays evolved as extensions of factorial plans and latin squares. This paper illustrates the fractional factorial nature of Taguchi's two-, three-, four-, and five-element orthogonal arrays. Similarly Taguchi's mixed-element orthogonal arrays define fractionated multi-level factorial plans. Thus Taguchi's orthogonal arrays are an element in the continuum of the development and use of statistically planned experiments.