23: Fractional Factorial Designs
"Among the factors to be considered there will usually be the vital few and the trivial many." - Turan.
"For there are hundreds of thousands of engineers in this country, and even if the 2^3 design was the only kind of design they ever used, and even if the only method of analysis that was employed was to eyeball the data, this alone could have an enormous impact on experimental efficiency, the rate of innovation, and the competitive position of this country." - George Box.
Lecture outline: how to conduct experiments in which multiple factors are changed simultaneously?
2(k-p) fractional factorial designs
1. Two level fractional factorial designs: model and analysis
Motivation of two-level fractional factorial designs
Example of 2(7-4) design
Balanced and Orthogonal designs
Model for fractional factorial design
Calculation of effects
Sign table for 2(k-p) design
Why fractional designs work?
2. Confounding and design resolution
Comparing fractional designs
Algebra of confounding
3. What is possible with 8 experimental runs (2-level designs)?
Single factor design with four replications
Two factor design with two replications
Three factor design with a single replicate
Four factor fractional factorial design with a single replicate.
Primary reference for this lecture:
“The Art of Computer Systems Performance Analysis: Techniques for Experimental Design, Measurement, Simulation, and Modeling” by Raj Jain; Selection sections from Chapters 21, 22, 23.