Example w/o interactions
Example 1: Perform the analysis for five 3-level factors without interaction based on two replications and a nominal target of 40.
We can use the L18 23 design described in 3-level Taguchi Designs leaving the 2-level column blank, as shown in Figure 1 and continuing in Figure 2.
Figure 1 – L18 23 design (part 1)
Figure 2 – L18 23 design (part 2)
We see that the optimum design is A1B2C1D3E3 which provides a 1.75928 deviation from the target of 40.
We can also use the formula =TOptimize(O3:R7,U3:V7,40,TRUE,FALSE) to list all the combinations for the retained factors A, B, and D, as shown in Figure 3.
Figure 3 – Factor combinations
Example with interactions
Example 2: Show how to set up the design of three 3-level factors along with their pairwise interactions.
We can use the L27 3 design as shown in Figure 4 (only the first few rows are displayed).
Figure 4 – 3-level design with interactions
We place factors A and B in columns 1 and 2. Since =TIinteract(1,2,3) returns the row array 3, 4, we place the interaction AB in columns 3 and 4. Since all the factor labels need to be unique, we need to place the labels AB in columns 3 and 4 but with some distinct third symbol appended to AB.
We now place factor C in column 5. Since =TInteract(1,5,3) returns the row array 6, 7, we place AC1 and AC2 in columns 6 and 7. Since =TInteract(2,5,3) returns 8, 11, we place BC1 and BC2 in columns 8 and 11.
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
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/