Full Factorial and Fractional Designs

Posted on November 10, 2009 by


Would almonds, pistachios, or peanuts taste best in the new ChocoNut Cookie being launched by Katy’s Cookie Factory? And should sugar or honey be used as a sweetener? There are two factors here—nut type and sweetener type. There are three levels of the nut factor (almonds, pistachios, and peanuts) and two levels of the sweetener factor (sugar and honey). Katy decides to create samples of cookies to give to customers so she better understands the Voice of the Customer before launching the product. What kinds of cookies should she make? There are six possible combinations—almonds-sugar, pistachios-sugar, peanuts-sugar, almonds-honey, pistachios-honey, and peanuts-honey. If you were to suggest that she make all six kinds of cookies, you are recommending a Full Factorial design. A Full Factorial design examines every combination of all levels of the experiment’s factors. A Fractional design examines only some of these combinations. So if Katy’s subject matter experts tell her that honey would taste terrible with almonds or pistachios and she decides to exclude those combinations, she now has four conditions in her experiment (almonds-sugar, pistachios-sugar, peanuts-sugar, and peanuts-honey) and it is a Fractional design.

Another example would be a study to measure the percentage of defective cookies made across four factory locations which each have three shifts. There are 12 possible combinations of each factory location and each shift. If defects are measured across all 12 combinations, it is a Full Factorial. However, if they decide to exclude the third shift for two of the factory locations, it is now a Fractional design.


Posted in: Six Sigma