5. Process Improvement
5.6. Case Studies
5.6.2. Sonoluminescent Light Intensity Case Study

## Interaction Effects

Check for Interaction Effects: DOE Interaction Plot In addition to the main effects, it is also important to check for interaction effects, especially 2-factor interaction effects. The DOE interaction effects plot is an effective tool for this.

Conclusions from the DOE Interaction Effects Plot We make the following conclusions from the DOE interaction effects plot.
1. Important Factors: Looking for the plots that have the steepest lines (that is, the largest effects), and noting that the legends on each subplot give the estimated effect, we have that

• The diagonal plots are the main effects. The important factors are: X2, X7, X1, and X3. These four factors have |effect| > 60. The remaining three factors have |effect| < 10.

• The off-diagonal plots are the 2-factor interaction effects. Of the 21 2-factor interactions, 9 are nominally important, but they fall into three groups of three:

• X1*X3, X4*X6, X2*X7 (effect = 70)
• X2*X3, X4*X5, X1*X7 (effect approximately 63.5)
• X1*X2, X5*X6, X3*X7 (effect = -59.6)

All remaining 2-factor interactions are small having an |effect| < 20. A virtue of the interaction effects matrix plot is that the confounding structure of this Resolution IV design can be read off the plot. In this case, the fact that X1*X3, X4*X6, and X2*X7 all have effect estimates identical to 70 is not a mathematical coincidence. It is a reflection of the fact that for this design, the three 2-factor interactions are confounded. This is also true for the other two sets of three (X2*X3, X4*X5, X1*X7, and X1*X2, X5*X6, X3*X7).

2. Best Settings: Reading down the diagonal plots, we select, as before, the best settings "on the average":

(X1,X2,X3,X4,X5,X6,X7) = (+,-,+,+,+,-,-)

For the more important factors (X1, X2, X3, X7), we note that the best settings (+, -, +, -) are consistent with the best settings for the 2-factor interactions (cross-products):

X1: +, X2: - with X1*X2: -
X1: +, X3: + with X1*X3: +
X1: +, X7: - with X1*X7: -
X2: -, X3: + with X2*X3: -
X2: -, X7: - with X2*X7: +
X3: +, X7: - with X3*X7: -