The following figures list the 2-level Taguchi designs supported by Real Statistics.
Designs
Smaller designs:
Figure 1 – L4, L8, L12 designs
Larger designs:
Figure 2 – L16 design
Figure 3 – L32 design
Efficiency of Taguchi designs
A full factorial experiment with 7 factors requires 27 = 128 test runs. Taguchi’s L8 design supports a fractional factorial experiment with only 8 test runs.
Similarly, a full factorial experiment with 15 factors requires 215 = 32,768 test runs. Taguchi’s L16 design supports such an experiment with only 16 test runs.
Interactions
We mentioned in 2-level Taguchi Design that only certain columns can be used for the interaction between two factors. For the 2-level designs shown above, L12 doesn’t permit the interaction of factors. For the other four designs, Figure 4 displays the permissible interactions.
Figure 4 – Interactions for 2-level factors
E.g. if we place main effects factors in columns 3 and 7 of an L8 design, we can only place the interaction between these two factors in column 4 (see cell G4). Similarly, if we place main effects factors in columns 7 and 10, then we can only place the interaction between these two factors in column 13 (see cell J8).
This explains why we placed the interaction AB for Example 1 of 2-level Taguchi Design in column 3 of Figure 2 on that webpage and the interaction BC in column 6.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
References
Roy, R. K. (2010) A primer on Taguchi method. 2nd ed. Society of Manufacturing Engineers
https://brharnetc.edu.in/br/wp-content/uploads/2018/11/11.pdf
University of York (2004) Orthogonal arrays (Taguchi designs)
https://www.york.ac.uk/depts/maths/tables/orthogonal.htm
Minitab (2024) Catalogue of Taguchi designs
https://support.minitab.com/en-us/minitab/help-and-how-to/statistical-modeling/doe/supporting-topics/taguchi-designs/catalogue-of-taguchi-designs/