Problem:
Let’s consider a real problem where an engineer is studying the effect of seven factors on the yield of a chemical reaction process (catalyst level, pressure, purity, reaction time, solvent, stirring rate, and temperature). The yield is the response expressed as a percent of theoretical.

Solution:
The fractional factorial design use is listed in Table 1 (Note this is not a ‘one factor at a time’ experiment).

The yields for each experiment are at the extreme right of the table and vary from a low of 50% to a high of 88%. But what is causing the higher yields?

The best way to answer this question is to look at the table of effects. An effect is the change in the yield when a particular factor is moved from it’s highest level to it’s lowest while keeping all other factors at a constant level. This is calculated from the model.

Table 2 shows the effects for each of the seven factors in our experiment.

But which of these effects are really significant and which are so small that they can just be thought of as the result of random fluctuations? One good way to look at this is to plot the effects on a normal probability plot. In a normal probability plot of effects, those which are important will be found far from the other effects which will be hovering around zero. Figure 1 shows our seven effects plotted. Note that Stirring Rate and Temperature are the large effects and have the most effect on yield.

Note that both effects are negative. Since it is desirable to maximize the yield, then the proper settings for these two factors is at their high levels. If you set them both high while leaving the other five (non-significant) factors at their low levels, you get a predicted yield of 82%.

So, what have we learned from this small experiment and the subsequent analysis of the yield data? In terms of the technology, we discovered that two factors (Stirring Rate and Temperature) were highly influential in obtaining high yields and that the other five factors made essentially no contribution. In terms of statistics, we learned that a fractional factorial design can be a very efficient way of screening factors in any system and finding the important ones.