Why Use Taguchi Methods?

“Why use Taguchi methods?” - that is the first question most people ask when told about our software. The short answer is it allows you to quickly optimize your website conversion. That may be all you need to know, but I’m going to give a much more detailed answer.

The Taguchi method was developed by Dr. Genichi Taguchi. After World War II he was employed by the Japanese Ministry of Public Health and Welfare to work on the first national study of health and nutrition. This work led him to Morinaga Pharmaceutcal  where he explored efficient experimentation techniques to develop methods for producing penicillin. This work led to his application of orthogonal arrays for designing efficeint experiments and analyzing experimental data. Now whenever orthogonal arrays are used in experimental design, it is referred to as the Taguchi Method.

The orthogonal array allows for significant reduction in the number of experimental runs to find the optimal solution. For example, testing 15 factors each having 2 levels requires 16 experimental runs compared to 32,768 required using standard methods such as Google Website Optimizer. So what makes the orthogonal array so special?

First I should probably explain what is orthogonality means. Simplest definition is it means balanced and not mixed. In the context of test arrays it means statistically independent. Mathematically is means the dot product of any two vectors made from the columns of the test array is zero. Now that will make your head hurt! Let’s take a look at the L8 orthogonal array shown below.

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

First note that in each column level 1 occurs four times and level 2 occurs 4 times. This is true for any number of levels in an orthogonal array. There will aways be an equal number of occurrences of each level. Also look at columns 1 and 2 and notice that values of levels in column 2 have equal occurrences for each level in column 1. That is when column 1 is level 1, then column 2 has level1 twice and level 2 twice. This is the same for level 2 in column 1. It is this nature of the orthogonal array that allows levels in each column to be studied independent of levels in other columns. That make the array orthogonal.

Now let’s look at it from a mathematical viewpoint. We will set value of level 1 to -1 and value of level 2 to 1.  Now let’s do dot product of column 1 and 2. (-1 x -1)+(-1 x -1)+(-1 x 1)+(-1 x 1)+(1 x -1)+(1 x -1)+(1 x 1)+(1 x 1) = 0 Recall the dot product of any pair of vectors from columns of the array must be zero for the array to be orthogonal. This mean the vector are perpendicular and therefore statistically independent.

So now I hope you can appreciate the power of the orthogonal array. It allows evaluation of each level of a factor independent of values of other factors. This property leads to reduction of the test runs necessary to cover all the combinations of factors and their levels resulting in quicker testing to achieve optimal website conversion.