Proposal of Advanced Taguchi’s Linear Graphs for Split-Plot Experiments

Taguchi’s orthogonal arrays and linear graphs are convenient tools for the design of fractional factorial experiments, especially for practitioners. Taguchi also proposed how to use them in split-plot designs and prepared linear graphs for split-plot designs. For the orthogonal array of order 16, Taguchi proposed one which is called L₁₆ orthogonal array. Taguchi presented 18 linear graphs when a L₁₆ orthogonal array is used in split-plot designs. Those linear graphs are capable of showing main effects of whole plots, subplots, sub-subplots, and so on, but they are not capable of showing interaction effects of plots of different levels. Also, those linear graphs do not cover all the possible designs, and there exist a lot of other linear graphs that can be applied when using L₁₆ orthogonal arrays. The primary objective of this paper is to propose an improved version of linear graphs. Another purpose of this paper is to investigate how to list all the possible linear graphs that can be applied when using L₁₆ orthogonal arrays. A proposal is made and many new linear graphs are presented.