1. 1 The One-Quarter Fraction of the 2 k

2. 2 The One-Quarter Fraction of the 2 6-2 Complete defining relation: I = ABCE = BCDF = ADEF

3. 3 The One-Quarter Fraction of the 2 6-2 Uses of the alternate fractions E = ±ABC, F = ±BCD Projection of the design into subsets of the original six variables Any subset of 4 factors of the original 6 variables that is not a word in the complete defining relation will result in a full factorial design Any subset of 4 factors of the original 6 variables that is a word in the complete defining relation will result in a replicated one-half factorial design –Consider ABCD (full factorial) –Consider ABCE (replicated half fraction) –Consider ABCF (full factorial)

4. 4 Design Matrix of Example 8-4 Injection molding process with six factors

5. 5

6. 6 Large effects: A, B, and AB (Ockham’s razor) The process is sensitive to temperature (A) if the screw speed (B) is at the high level => both A and B should be at the low level (reduce mean shrinkage) How about the part-to-part variability?

7. 7 ŷ =  o +  1 x 1 +  2 x 2 +  12 x 1 x 2 =  +  x 1 +  x 2 +  x 1 x 2 e = y - ŷ

8. 8 Residual plots indicate there are some dispersion effects, which can be quantified by an analysis of residuals.

9. 9 Example 8-4 Factor C has a large dispersion effect. Its location effect is not large, so its level can be set to low to reduce variation.

10. 10 Projection onto a cube in A, B, and C (Example 8-4) 2 6-2 -> 2 3 (n=2) B=low results in low values of average part shrinkage C=low produces low part-to-part variation => B - C - 10