Understanding full factorial design
One of the fundamental types of experimental designs is the full factorial design. This post will explore what a full factorial design is, its benefits, and why it is not always a good idea to use a full factorial design.
What is a Full Factorial Design?
A full factorial design is a type of experimental design used in DoE. It combines each factor at each level with every other factor and level to test their individual and combined effects on the response variable.
Example:
Consider an experiment with two factors: Temperature (T) and Concentration of Catalyst (C). Each factor is studied at two levels: low (-1) and high (+1). We want to measure the effect of these factors on the yield of a chemical reaction.
Typically, we might change one factor at a time (OFAT) and test how each individual factor affects the yield. However, with a full factorial design, we also test combinations where both temperature and concentration are at their high levels. In this full factorial design, each level of temperature is tested at each level of concentration.
What does a full factorial design that OFAT designs don’t?
If we had executed an OFAT (One Factor At a Time) design, we might have concluded that higher concentrations of catalyst and higher temperatures increase the yield. The conclusion could be that, in the future, we run the reaction at higher temperatures with a high concentration of catalyst. But here’s the problem:
With OFAT, we didn’t test the combination where both factors were at their high levels. But with a full factorial design, we did.
There we see that there is an interaction between temperature and concentration, which means that the effect of concentration depends on the temperature. At 100 degrees, the increase in concentration positively influences the yield. However, at the high temperature, the increase in concentration actually decreases our yield. This is why full factorial designs are so powerful. Because they capture such interactions.
Interactions like this occur frequently in experiments. Understanding these interactions helps in optimizing processes and achieving better outcomes. But full factorial designs also have limitations.
The problem with full factorial designs
The primary issue is the number of runs required when many factors are involved, especially when more than two levels are included. The number of runs grows exponentially with the number of factors and levels. For example, a full factorial design with three factors, each at three levels, would require 27 runs (3^3). This quickly becomes impractical for a large number of factors or levels.
Therefore, other design plans, such as fractional factorial designs or central composite designs (CCD), can be used instead of full factorial designs to reduce the number of runs while still obtaining useful information. That’s what we will take a look at in our next blog post.
