I answer questions about the "orthogonal table" used in quality engineering(QE) experiments.
This is the explanation material. → QE18
p.1: I will explain my interpretation about the three questions in three times.
p.2: Q1 "Why does the orthogonal table experiments can show the magnitude of the effect of the level of each factor on the SN ratio?" To simplify the explanation, I assume the "graph of factorial effects" for the control factors A, B, C and D looks like figure . The average value is set to zero.
p.3: In QE, we do not use the L9 “orthogonal table” because interactions easily occur, but I explain it using it to simplify. The upper left is the allocation table of the orthogonal table. The figure at the lower left is obtained by substituting the SN ratio of each control factor's level shown in p.2. Dividing into groups of experiments 1 to 3, experiments 4 to 6 and experiments 7 to 9, focusing only on the control factor A, A1 is (10+10+10)/3=10, A2={(-6)+(-6)+ (-6)}/3=-6, and similarly A3=-4. On the other hand, the effects of B, C, and D are 0 (zero), and you can see that the effects of levels 1, 2, and 3 can be evaluated if you focus only on column A.
p.4: The same applies to control factor B. The experiments on B1 are 1, 4 and 7, B2 are experiments 2, 5 and 8, and B3 are experiments 3, 6 and 9, and every sums of B1, B2 and B3 are averaged. The same applies to both L12 and L18 orthogonal tables.