Box–Behnken designの英語

In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals:

• Each factor, or independent variable, is placed at one of three equally spaced values. (At least three levels are needed for the following goal.)
• The design should be sufficient to fit a quadratic model, that is, one containing squared terms and products of two factors.
• The ratio of the number of experimental points to the number of coefficients in the quadratic model should be reasonable (in fact, their designs kept it in the range of 1.5 to 2.6).
• The estimation variance should more or less depend only on the distance from the centre (this is achieved exactly for the designs with 4 and 7 factors), and should not vary too much inside the smallest (hyper)cube containing the experimental points.