This is a graph contain seven various factors. Generally to find out the most important factor in full factorial experiment, it takes 128 times experiments. However, the way of orthogonal arrays achieve this goal in only 8 times experiments.
in my opinion, it is realized through the concepts of ‘average’ and ‘group’. For example, when testing the importance of factor A, this tool takes the same A as a whole group, in every A group there are equal amount of same kind of B, C, D, E, F, G. By this way, these ‘different’ factors (B-G) are transfer to be the ‘same’. This is similar to the tool of ‘single factor control variates’ but with seven factors in fact.
The most interesting thing in this table is that no matter which factor you take into consideration, the number of same kind of other factors is always equal to 4(factor number=7).
In order to consider the interaction within two factors, the relationships can be abstractly concluded into ‘same’ and ‘different’. This relationship is put into the system orthogonal arrays again as an independent factor.