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

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

Example 8-1

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

Ex. 8-1. A projection with 1 replicate Ex. 6-2. A projection with 2 replicates

Regression Model y = bo + b1x1 + b3x3 + b4x4 + b13x1x3 + b14x1x4 Regression model developed in Ex. 6-2 Filtration Rate = +70.06250 +10.81250 * x1 +4.93750 * x3 +7.31250 * x4 -9.06250 * x1x3 +8.31250 * x1x4

Example 8-2

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

Example 8-3