Using Plackett–Burmans to construct a 16 factor design (see below) requires only 221 points. A design for 16 factors exists having only 256 factorial points. Designs for other numbers of factors have also been invented (at least up to 21). Taking the 9 factor design, deleting one column and any resulting duplicate rows produces an 81 run design for 8 factors, while giving up some "rotatability" (see above). The design for 8 factors was not in the original paper. In this table, m represents the number of factors which are varied in each of the blocks. It is necessary to include centre points as well (in which all factors are at their central values). For instance, the Box–Behnken design for 3 factors involves three blocks, in each of which 2 factors are varied through the 4 possible combinations of high and low. In each block, a certain number of factors are put through all combinations for the factorial design, while the other factors are kept at the central values. The design with 7 factors was found first while looking for a design having the desired property concerning estimation variance, and then similar designs were found for other numbers of factors.Įach design can be thought of as a combination of a two-level (full or fractional) factorial design with an incomplete block design.
AXIAL FONT BOX FULL
(See "rotatability" in " Comparisons of response surface designs".)īox-Behnken design is still considered to be more proficient and most powerful than other designs such as the three-level full factorial design, central composite design (CCD) and Doehlert design, despite its poor coverage of the corner of nonlinear design space.
Box and Donald Behnken in 1960, to achieve the following goals: In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. Experimental designs for response surface methodology
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