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Box-Behnken design
Designs for Constrained Situations, General Principles
This chapter introduces “tricky” situations in which classical designs based upon the factorial principle do not
apply. Here, you will learn about two specific cases:
1.
Constraints between the levels of several design variables;
2.
A special case: mixture situations.
Each of these situations will then be described extensively in the next chapters.
Note: To understand the sections that follow, you need basic knowledge about the purposes and principles of
experimental design. If you have never worked with experimental design before, we strongly recommend that
you read about it in the previous sections (see What Is Experimental Design?) before proceeding with this
chapter.
Constraints Between the Levels of Several Design Variables
A manufacturer of prepared foods wants to investigate the impact of several processing parameters on the
sensory properties of cooked, marinated meat. The meat is to be first immersed in a marinade, then steam cooked, and finally deep-fried. The steaming and frying temperatures are fixed; the marinating and cooking
times are the process parameters of interest.
The process engineer wants to investigate the effect of the three process variables within the following ranges
of variation:
Ranges of the process variables for the cooked meat design
Process variable
Low
High
6 hours
18 hours
Steaming time
5 min
15 min
Frying time
5 min
15 min
Marinating time
A full factorial design would lead to the following “cube” experiments:
The cooked meat full factorial design
Sample
Mar. Time
Steam. Time
Fry. Time
1
6
5
5
2
18
5
5
3
6
15
5
4
18
15
5
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Principles of Data Collection and Experimental Design 25