Study Interactions Using The Taguchi Method

A rarely discussed and utilized property of the Taguchi Method is the study of interactions. Dr. Taguchi incorporated additional power in the use of orthogonal arrays for test design via the linear graph. Using these linear graphs it is possible to assign factors to the correct columns in order to study interactions between the factors while also revealing the effects of the individual factors.

Although it is not possible to study all interactions as can be done with the full factorial test, you can use your knowledge of likely interactions and test their impact. You can also set up the test to study interactions just to see if one exist. This can led to some interesting results.

To understand how this is done, let’s look again at the L8 orthogonal array.

Experiment	Columns
Number	1	2	3	4	5	6	7
1	1	1	1	1	1	1	1
2	1	1	1	2	2	2	2
3	1	2	2	1	1	2	2
4	1	2	2	2	2	1	1
5	2	1	2	1	2	1	2
6	2	1	2	2	1	2	1
7	2	2	1	1	2	2	1
8	2	2	1	2	1	1	2

Here are the two linear graphs that can be used for this array.

The dots are labeled with the array column for factor and the connecting line is labeled with the column used for the interaction. The graph on the left shows that 3 interactions between factors assigned to array columns 1, 2 and 4 can be studied. This means that a total of 4 factors and 3 interactions are available using that linear graph and no interaction associated with factor assigned to column 7 . The graph on the right shows that 3 interactions between factor assigned to column 1 and factors assigned to columns 2, 4, and 7. Using these linear graphs provide a logical scheme for assigning factors and interactions without confounding the effect of the interaction with the effect of the factors.

Our software lets you pick the interactions you want to study and then it selects the appropriate Taguchi array. This means you don’t have to learn all the details of this process but can use its power.

Not all the Taguchi arrays allow for the study of interactions. Here is a summary of the properties of each array but first let’s review the terminology. The standard terminology for an orthogonal array takes the form L_a(B^c). The subscript of L represents the number of experimental runs or combination of factors that can be conducted in the test. B is the number of levels in each column and its c exponent is the number of columns in the array.

• L₄(2³) is actually a full factorial array of 2 test factors and an interaction between them. If it is know that the interaction is weak or not present, then a third factor can be assigned to the third column. It has 1 linear graph.
• L₈(2⁷) is a very flexible array that allows for 7 factors and interactions to be studied.It has 2 linear graphs as shown above.
• L₁₂(2¹¹) is unique in that the effect of interactions are distributed evenly across all columns. This minimizes the possibility of confounding effects of factors and interactions, but eliminates the ability to study interactions.
• L₁₆(2¹⁵) allows for 15 factors and interactions to be studied. It is often used in place of the L₁₂(2¹¹) array when you need to study interactions. It has 18 linear graph.
• L₃₂(2³¹) allows for 31 factors and interactions to be studied. It has 39 linear graphs.
• L₉(3⁴) allows for 4 factors or 2 factors and one interaction. It has 1 linear graph.
• L₁₈(2¹ X 3⁷) is unique in several ways. One is the first column in 2 level and the other 7 are 3 level. It is similar to L₁₂(2¹¹) in that interactions are distributed evenly across all columns except columns 1 and 2. The interaction between factors assigned to column 1 and column 2 can be studied using a 2X3 response table and does can require use of another column for interaction. It has 1 linear graph. This is the array modified by Dr. Kowalick and used incorrectly by most testing software.
• L₂₇(3¹³) allows for 13 factors or 7 factors and 3 interactions or 5 factors and 4 interactions. It has 3 linear graphs.
• Other arrays are:
  • L₆₄(2⁶³) It has 30 linear graphs.
  • L₅₄(2¹ X 3²⁵) It has 1 linear graph.
  • L₈₁(3⁴⁰) It has 42 linear graphs.
  • L₁₆(4⁵) It has 1 linear graph.
  • L₃₂(2¹ X 4⁹) It has 1 linear graph.
  • L₆₄(4²¹) It has 2 linear graphs.
  • L₂₅(5⁶) It has 1 linear graph.
  • L₅₀(2¹ X 5¹¹) It has 1 linear graph.

As you can see, the Taguchi Method allows for a full range of factors and interactions to be used in testing. This power is available in our software and cannot be found in others. It sort of compares to our software being on the level of the iPhone and all the others are using rotary dial hand sets