RSM Simplified: Optimizing Processes using Response Surface Methods for Design of Experiments

Practice Problems

PROBLEM 8-1

University of Minnesota food scientists (Richert et al., 1974) used a central composite design to study the effects of five factors on whey protein concentrates, a popular diet supplement for body builders. Also, whey proteins, when properly processed, are beneficial in the development of foams characteristic of frozen desserts, whipped toppings, meringues, and mousses.

WHERE THERE'S A WHEY

Whey is the watery part (called the "serum") of milk that is separated from the curd in making cheese. Unless you work in the dairy industry (or engage in body-building), your only familiarity with this term may be from the nursery rhyme:

"Little Miss Muffet, sat on a tuffet,

Eating her curds and whey.

Along came a spider,

Who sat down beside her,

And frightened Miss Muffet away."

PS. A "tuffet" is either a mound of earth or a three-legged stool. (Source: http://nurseryrhymes.allinfoabout.com/missmuffet.html.)

The factors, with ranges noted in terms of alpha (star levels), were:

  1. Heating temperature: 65 to 85 C/30 min.

  2. pH level: 4 to 8.

  3. Redox potential: -0.025 to 0.375 volts.

  4. Sodium oxalate (Na 'Ox'): 0 to 0.05 molar.

  5. Sodium lauryl sulfate (Na LS): 0 to 0.2 percent of solids.

There were nine responses, but we will look at only three:

  1. Whipping time in minutes (to produce a given amount of foam).

  2. Time at first drop in minutes (a measure of foam stability).

  3. Undenatured protein in percent.

Denature means to render unfit, so therefore the undenatured protein must be maximized. The whipping time should be minimized...

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