# Quality engineering(QE) 8

It is finally an orthogonal table experiment, but the evaluation result is not the output itself, but the SN ratio. Probably learner may not understand the meaning of this SN ratio formula, and I wonder if they avoid quality engineering(QE). I can't explain SN ratio formula well same as you. For the time being, I try to make the figure as easy as possible to make it easier to imagine. I'm not satisfired yet, but please refer to the following materials.

Click attachment →　QE8

p.1: The SN formula is the formula in the square frame below, and Ve is subtracted because it is estimating the expected value. What I want you to remember here is that the numerator is the signal (effective component) and the denominator is the noise (non-effective component).

p.2: In QE and analysis of variance, using the sum of squares makes it easier to imagine. In this example, it is set that there are data of y1 = 5, y2 = 4, y3 = 3 for the target value m. The sum of squares of these data is ST = 25 + 16 + 9 = 50 and is called "total variation ST". The average value(y bar) is 4 for y1, y2 and y3. The sum of squares of deviation from the target value is Sm = 16 + 16 + 16 = 48. The sum of squares of the difference between this average value and y value is the error fluctuation Se = 1 × 1 + (-1) × (-1) = 2. ST= Sm + Se, you know that is 50 = 48 + 2.

p.3: For a straight line with a target slope of 1, if all three y data is 2, the total variation ST = 2 × 2 + 2 × 2 + 2 × 2 = 12. The slope variation Sβ is calculated by the formula on p.4. There are two, L1 and L2, but in the case of p.3, you use only to L1. L1 is that you multiply the signal by data and sum them. L1 = 1 × 1 + 2 × 2✛3 × 3 = 14. You divide squared 14 divided by sum of the square of the signal and get approximately 10. The difference between the straight line and the data y is an error. Sum of squares of error Se = 1 × 1 + 0 × 0 + (− 1) × (−1) = 2 . Again, ST= Sβ + Se, that is, 12 = 10 + 2. Here too, the "additivity of sum of square " holds.

p.4: For the error factors N1 and N2, the data of the signals M1, M3 and M5 are as shown in the table. You calculate by below formulas and get SN ratio. New term SN × β and SN are added. In the case of molding, "the standard SN ratio method" is used, so use the formula on the lower left for the SN ratio. Usually,please use the lower right for the formulas for SN ratio and sensitivity.

p.5: The relation of the datas on p.4 is drawn on the graph. The meaning of SN × β shows the variation in the difference of the straight line between N1 and N2. We try to find the condition of minimum this difference by orthogonal table experiment.

p.6: It is a band graph. There is a slope variation(Sβ) and an error variation(Se) for N1 and N2, and there are difference variation( SN × β) of two straight line. SN is equivalent to the error variation, that is, the denominator of the SN ratio.