About TCAW - Subscription Info
February 2002
Vol. 11, No. 2
pp 21, 23–24.
Computers in Chemistry
The knead for speed

Design of experiments shows how to avoid failures in machine-made bread.

For years, I produced bread using premade mixes that were specifically formulated for use in bread machines. I recently decided that it would be more economical—and fun—to buy the ingredients separately. I wanted to see if I could save money by using the regular (and cheaper) varieties of flour and yeast rather than those developed specifically for bread machines. Also, according to a suggestion on the bread flour package, I could economize by using margarine and water instead of butter and milk. However, I thought I’d better do a proper design of experiments (DOE) to be sure my bread machine could handle all these variations in ingredients. The results of this DOE proved to be very informative, not only for avoiding breadmaker failure, but also for learning about the statistical methods.

My choices for ingredients can be seen below (coded minus and plus).

Liquid: water (–) or milk (+)
Oil: butter (–) or margarine (+)
Flour: regular (–) or bread (+)
Yeast: regular (–) or bread (+)

Ruggedness Testing
My need for speed precluded baking the 16 loaves required for all the combinations (the full two-level factorial design), so I chose a standard half-fraction requiring only eight runs (1). A DOE such as this works well for ruggedness testing, in which you expect nothing to be significant (2). In this case, I hoped that changing ingredients would produce negligible changes in the quality of the bread, thus allowing me flexibility in choosing whatever might be handy or cheap. This is also a nice way to prove that a change would be insignificant before an industrial scale-up.

First Breadmaking DOE: Half-Fraction Two-Level Factorial
# A: Liquid B: Oil C: Flour D: Yeast Rise?
1a,b Water Butter Regular Regular N, N
2a,b Milk Butter Regular Bread Y, Y
3a,b Water Margarine Regular Bread N, N
4 Milk Margarine Regular Regular Y
5 Water Butter Bread Bread Y
6 Milk Butter Bread Regular Y
7 Water Margarine Bread Regular Y
8 Milk Margarine Bread Bread Y
For the first run, I added the liquid, oil, flour, and yeast at specified levels (see Table 1), as well as salt and sugar (according to the recipe), and set the machine to bake overnight. The resulting bread looked good, but my taste panel (three daughters, one exchange student, and my wife) did not like it much. They gave it an average rating of 4.5 on a scale of 1 to 10. This would not do! I needed to adjust the recipe to get in a more desirable range of taste or face a possible strike by my tasters. I’d endured bad reviews in a previous DOE on baking a pound cake (3) and learned that adding more sugar made my testers more agreeable. So I upped this ingredient from 2 teaspoons to 2 tablespoons. The reviews sweetened up considerably and I started over with the eight-run DOE.

Surprisingly, in some cases the bread failed to rise (noted as “N” in Table 1). I repeated these combinations and got the same kind of failure. On the other hand, the bread came out fine with the majority of combinations (labeled “Y”). It’s important to note that the actual run order was randomized to avoid bias from time-related variables lurking in the background, such as machine wear.

Which of the tested ingredients, if any, caused the yeast to slack off, resulting in the unrisen bread? With the aid of statistical software for DOE (4), I saw an abnormally large (and highly significant) effect caused by the interaction of the liquid (A) and the flour (C). The combination of water and regular flour appeared to create problems with the breadmaker (zero rise at these conditions). However, a computer-aided evaluation of my DOE revealed that, by doing only 8 of the 16 combinations of ingredients, I created an aliasing of the AC interaction with the BD interaction, which made it impossible to be certain AC was the culprit.

First Breadmaking DOE: Design Layout in Coded Levels with Interactions Shown
1a,b + + + + + + N, N
2a,b + + + + + Y, Y
3a,b + + + + + N, N
4 + + + + Y
5 + + + + + Y
6 + + + + Y
7 + + + + Y
8 + + + + + + + + + + + Y
Factor Coding

Take a look at Table 2, which lays out the experimental design in coded levels with all interaction columns included. The factor coding is simple: minus (–) for one level versus plus (+) for the other. The coding for interaction columns is done by multiplying parent terms. For example, the AC column is computed by multiplying the A by the C column.

The peculiar thing about this matrix is that A times C equals B times D. These two interactions are therefore statistically “aliased”. It’s impossible to say which one is really causing the significant effect on breadmaking performance because they change back and forth from one level to the other in exactly the same pattern (see italicized columns in Table 2). With close inspection, you’ll notice that all of the two-factor interactions are aliased: AB = CD and AD = BC. It also turns out that all main effects get aliased with a three-factor interaction (for example: A = BCD; not shown in Table 2, but easily computed by multiplying B x C x D). However, it’s a generally acceptable practice to ignore interactions of three or more factors, because they’re so unlikely.

To resolve this aliasing problem, I had to do more runs. I made use of a nifty DOE method called a “semifold”, which requires adding only half the runs of the original design. This technique was developed specifically to improve resolution of two-level fractional factorial designs, such as that which I used for my breadmaking experiment. For background on the semifold method and many other statistical details, see references 5, 6, and 7, which also provide many helpful illustrations not shown here because of lack of space.

Semifold on Breadmaking Experiment
9 + + + + N
10 + + + + Y
11 + + + + N
12 + + + + + + Y
Table 3 shows the four new combinations tested in the semifold of my original DOE. Notice that the combinations of levels for the factors (A, B, C, and D) differ from any that I ran initially. Furthermore, by running this particular set of runs, the pattern in column AC now differs from that of BC, so these interactions now become de-aliased.

After the semifold runs, it could be seen for sure that the combination of water (A–) and regular flour (C–) caused the bread to fail (zero rise). This finding is unequivocal because the semifold of four runs de-aliased the interaction of factors A and C.

There’s always milk in the refrigerator at our home, so I just use it instead of water and the bread always rises. I use margarine and regular yeast with the regular flour to keep ingredient costs to a minimum. Unfortunately, because of the unexpected failures in getting my bread to rise, I lost sight of my original objective: improved taste. The statistical analysis (not shown here) does show a tendency for my family to prefer the same conditions that resulted in risen breads. However, some of my children actually rated the failed breads higher, which created ambiguity in the findings. They must like the gooey mouth feel of dough. (Yuck!)

I wish to thank Patrick J. Whitcomb, my partner at Stat-Ease, for inspiring me to experiment with the DOE methods detailed in this article.


  1. Anderson, M.; Whitcomb, P. DOE Simplified, Practical Tools for Experimentation; Productivity, Inc.: Portland, OR, 2000.
  2. Youden, W.; Steiner, E. Statistical Manual of the AOAC; Association of Official Analytical Chemists: Washington, DC, 1975.
  3. Anderson, M.; Whitecomb, P. Mixing It Up With Computer-Aided Design. Today’s Chemist at Work; 1997, 6 (10), 34–38.
  4. Design-Expert, version 6; Stat-Ease, Inc.: Minneapolis, 2000; www.statease.com.
  5. Anderson, M.; Whitcomb, P. How To Save Runs, Yet Reveal Breakthrough Interactions, by Doing Only a Semifoldover on Medium-Resolution Screening Designs; 55th Annual Quality Congress of the American Society of Quality: Milwaukee, WI, 2001.
  6. Anderson, M. Using DOE to Make Bread, Not Bricks (Or How to Bake Like a Pro). Stat-Teaser; Stat-Ease, Inc.: Minneapolis, June 2001; www.statease.com/newsltr.html.
  7. Anderson, M.; Bread DOE Part 2: Semifold Confirms Cause for Failure. Stat-Teaser; Stat-Ease, Inc.: Minneapolis, September 2001; www.statease.com/newsltr.html.

Mark J. Anderson is a principal at Stat-Ease, Inc., in Minneapolis. He earned B.S.Ch.E. and M.B.A. degrees at the University of Minnesota. Send your comments or questions regarding this article to tcaw@acs.org or the Editorial Office 1155 16th St N.W., Washington, DC 20036.

Return to Top
|| Table of Contents

 CASChemPortChemCenterPubs Page