# Quality engineering(QE) 12

Once you have completed all the orthogonal table experiments, you need to plot the raw data to see if you can use the SN ratio formula. This work is important. Please see the following materials.

p.1, 2: Normally, data is taken with dynamic characteristics, so let's plot the output against the input. You should be able to draw 18 graphs in the L18 orthogonal array experiment. Looking at these 18 graphs, select 3 from the one with good characteristic and 3 from the bad one. Good characteristic is L11, L18 and L2, bad one is L9, L1 and L10. A good characteristic means that the line of N1 and N2 are close to each other, and a bad characteristic means that the line of N1 and N2 are apart. Please check if a SN ratio is more larger in the good characteristic and a SN ratio is more smaller in the bad characteristic .　The thing to note here is the case of L2. Even though the SN ratio is large, there may be no sensitivity (straight line slope) at all. Please be careful.　The one that is close to the ideal is the one with high SN ratio and high sensitivity. It is important to check the raw data to see if the numbers are good or bad.

p.3: If the value of the SN ratio and the status selected from the graph match, draw a "graph of factorial effects" as the next step. Align the control factor and its level on the horizontal axis, and plot the SN ratio or sensitivity on the vertical axis.　The optimal conditions are combinations with a high SN ratio. Conversely, the worst is a combination with a low SN ratio.　In principle, the SN ratio is given priority over the sensitivity. 　Plan A is the optimum condition that prioritizes the SN ratio, and Plan B is the optimum condition that prioritizes the sensitivity. Optimal conditions are different. There are some pattern that priority may be given to SN ratio with sacrificing sensitivity or priority may be given to sensitivity with sacrificing SN ratio.

p.4: The table on the left shows the SN ratio entered as a numerical value for each row. For example, I explain how to obtain the SN ratios of levels 1, 2, and 3 for parameter B. Please compare the table on the right with the table on the left. The SN ratio including Level 1 is in the red frame. Since there are 6 data, the average value is calculated as B1, which is calculated as 49.619. Similarly, level 2 is the average of the SN ratios of 6 green frames, and level 3 is the average of 6 blue frames.　The other columns are calculated in the same way.　After calculating once, check that the average value of A to H and the average of all SN ratios are all the same. For different values, please check the formula.

p.5: A graph of factorial effects is one plotting the SN ratio for each factor level. After drawing, pick up the one with high SN ratio and the one with low SN ratio, and set them as the optimum condition and the worst condition, respectively.

p.6: The difference between the each sum of SN ratios for the optimum condition and for the worst condition is called the estimated gain.

p.7: Make samples under optimal and worst conditions, calculate the SN ratio, and calculate the confirmation gain. This optimum condition and the worst condition do not appear in the orthogonal table. The L18 orthogonal table represents 2×37=4,374 combinations on behalf of 18 combinations, so the optimum condition should be the condition with the highest SN ratio among the 4,374 combinations. However, the gain may be negative. In this case, it means that a graph of factorial effects cannot be trusted. It has to be necessary to repeat the experiment by changing the control factor or level again.