It’s the most wonderful time of the year – the time for holiday bakers and cookie monsters to unite! So what’s a quality improvement professional to do when his favorite sugar cookie recipe produced cookies that failed to hold their festive holiday shapes after being baked? Run a Design of Experiment (DOE), of course!

## A Fractional Factorial Experiment

Bill Howell, an avid baker and quality professional, used Minitab’s DOE tools to get to the bottom of his sugar cookie shape faux pas.

Howell planned to design an experiment that would allow him to screen many factors, determine which were most important, then adjust his process to get the results he wanted—in this case, to make cookies that still looked like snowmen when they came out of the oven.

He elected to run a fractional factorial experiment, a class of factorial designs that lets you identify the most important factors in a process quickly and inexpensively.

Howell’s experiment required him to make 8 runs (or batches of cookies) to assess six factors, each of which was tested at two levels:

• Oven temperature (325 or 375 F)
• Number of eggs in a batch (1 or 2)
• Ounces of AP Flour in a batch (9 or 13.5)
• Baking soda amount (0.5 or 1 teaspoon)
• Cream of Tartar amount (0.5 or 1 teaspoon)
• Chilling the dough after rolling and cutout (yes or no)

Howell took extensive steps to ensure a robust process. He used 3 different shape cutters to prepare the cookie dough for the oven, selecting measuring points on each cutter, and measuring them with a 6 inch caliper accurate to .001 inch. Each of the eight experimental batches included stars, snowmen and gingerbread men.

To ensure consistent dough thickness, Howell used wood strips to prevent his rolling pin from flattening dough any thinner than ¼ inch. To minimize undue influence or unintentional bias during the baking process, he randomized the placement of the cookies on the baking sheet. He also rotated the baking sheets 180° halfway through baking.

Because two oven temperatures were used in the experiment, baking times varied by trial. The actual cooking times for each trial were recorded on the trial instruction sheet.

Each trial consisted of baking two trays of cookies. When they came out of the oven, Howell measured two samples of each shape from both trays to see if there had been a change in overall height, a selected width measurement, or thickness. These dimensions were recorded on preprinted forms, which identified the trial number, data of trial, cutter shape, width and height. Howell calculated averages and standard deviations for each cutter shape, and used Minitab to analyze the data.

## DOE Results

An analysis of height and width measurements done in Minitab revealed that flour was the driving factor in spread of the cookie. “In each instance, a higher amount of flour produced less spreading from the original dimension,” Howell says. “Impact on cookie thickness was principally influenced by flour and the number of eggs in the batter. Two eggs produced more rise than one egg.”

Howell also used Minitab to create main effects plots, which examine differences among level means for one or more factors.

Howell’s main effects plots reinforced the findings of the analysis, and also revealed that cutter type had an effect. “The width measurement for the star-shaped cutter moved an average of .35 inches, but the Snowman moved an average .95 inches and the Gingerbread Man moved an average of .55 inch,” he says. “This indicates that the shape of the cutter affects the flow of the cookie dough as it bakes.”

Howell is confident the experiment he designed and analyzed using Minitab will result in better cookies in the holiday seasons to come. “Cutout cookie batches this holiday season will follow the methods and levels that worked best in the experiment—with maybe just another ½ oz of flour thrown in—as these held their shape nicely, and the people who sampled from this trial liked their taste.”

## Bill Howell’s Optimized Sugar Cookie Recipe

Howell’s recipe can be found at http://www.minitab.com/en-us/News/Sugar,-Spice,-and-Everything-Statistics--Using-Design-of-Experiments-to-Bake-a-Better-Cookie/. If you try the recipe, be sure to let us know how your cookies turn out. Happy Baking!

Have you ever used DOE to optimize a recipe? Let us know in the comments below.

Of possible interest:

How Statistics Got to the Root of My Turnip Soup Problem

Celebrating National Pierogi Day with DOE

Gummi Bear DOE