1. Construction of One-half Fractions
The basic design; the design generator

2. Projection of Fractional Factorials
Every fractional factorial contains full factorials in fewer factors
The “flashlight” analogy
A one-half fraction will project into a full factorial in any k – 1 of the original factors

3. Example 8-1

4. Example 8-1
Interpretation of results often relies on making some assumptions
Ockham’s razor
Confirmation experiments can be important

5. Ex. 8-1. A projection with 1 replicate
Ex A projection with 2 replicates

6. Regression Model y = bo + b1x1 + b3x3 + b4x4 + b13x1x3 + b14x1x4
Regression model developed in Ex. 6-2
Filtration Rate = * x * x * x * x1x * x1x4

7. Example 8-2

11. Possible Strategies for Follow-Up Experimentation Following a Fractional Factorial Design

12. Example 8-3