What is Fractional Factorial Design?

Video 1. What is Fractional Factorial Design of Experiments.

Fractional Factorial Design runs only a fraction of the full factorial design to screen the most important variables/factors that affect the response the most. For example, a 2⁷ design of an experiment with seven variables of two levels for each factor will require 128 unique experiments to complete one full replication of the design. Running 128 experiments will be unnecessary and wasteful. Therefore, a fraction of the 128 experiments is run first to understand whether all seven variables are affecting the response or not. For example, 1/16^th of the 128 experiments results in only eight experiments, which has seven degrees of freedom, and can be utilized to get enough information for the seven variables to screen out the most important ones. A stronger justification for the fractional factorial design of an experiment has been observed through the Principle of Factor Sparsity.

The Principal of Factor sparsity, Pareto Principal or the 80/20 Rule

Italian economist and sociologist Vilfredo Pareto (1848-1923) discovered that 80% of the wealth in Italy belonged to about 20% of the population. There are many situations that follow the same principle. Such as roughly 80% of effects come from 20% causes. Joseph Juran (1904-2008) suggested this principle as the Pareto Principle after the name of Vilfredo Pareto. In reality, only a few factors produce the significant effect in an experiment that involves many factors. In the design and analysis of experiments, the Pareto Principle is known as the Principle of Factor Sparsity (Box et al., 2005; Montgomery, 2019).