5. Process Improvement
5.5.9. An EDA approach to experimental design
5.5.9.10. DOE contour plot

## How to Interpret: Best Corner

Four corners representing 2 levels for 2 factors The contour plot will have four "corners" (two factors times two settings per factor) for the two most important factors Xi and Xj: (Xi, Xj) = (-, -), (-, +), (+, -), or (+, +). Which of these four corners yields the highest average response ? That is, what is the "best corner"?
Use the raw data This is done by using the raw data, extracting out the two "axes factors", computing the average response at each of the four corners, then choosing the corner with the best average.

For the defective springs data, the raw data were

X1 X2 X3 Y
- - - 67
+ - - 79
- + - 61
+ + - 75
- - + 59
+ - + 90
- + + 52
+ + + 87
The two plot axes are X1 and X3 and so the relevant raw data collapses to
X1 X3 Y
- - 67
+ - 79
- - 61
+ - 75
- + 59
+ + 90
- + 52
+ + 87
Averages which yields averages
X1 X3 Y
- - (67 + 61)/2 = 64
+ - (79 + 75)/2 = 77
- + (59 + 52)/2 = 55.5
+ + (90 + 87)/2 = 88.5
These four average values for the corners are annotated on the plot. The best (highest) of these values is 88.5. This comes from the (+, +) upper right corner. We conclude that for the defective springs data the best corner is (+, +).