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- Q4952019 subject Q6159380.
- Q4952019 abstract "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, usually coded as -1, 0, +1. (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. (See "rotatability" in "Comparisons of response surface designs".)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.Each design can be thought of as a combination of a two-level (full or fractional) factorial design with an incomplete block design. 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. 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. It is necessary to include centre points as well (in which all factors are at their central values).In this table, m represents the number of factors which are varied in each of the blocks.The design for 8 factors was not in the original paper. 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). Designs for other numbers of factors have also been invented (at least up to 21). A design for 16 factors exists having only 256 factorial points. Using Plackett–Burmans to construct a 16 factor design (see below) requires only 221 points.Most of these designs can be split into groups (blocks), for each of which the model will have a different constant term, in such a way that the block constants will be uncorrelated with the other coefficients.".
- Q4952019 wikiPageExternalLink handbook.
- Q4952019 wikiPageExternalLink pri3362.htm.
- Q4952019 wikiPageExternalLink pri3363.htm.
- Q4952019 wikiPageWikiLink Q12483.
- Q4952019 wikiPageWikiLink Q176691.
- Q4952019 wikiPageWikiLink Q1826488.
- Q4952019 wikiPageWikiLink Q2265984.
- Q4952019 wikiPageWikiLink Q2334061.
- Q4952019 wikiPageWikiLink Q3136137.
- Q4952019 wikiPageWikiLink Q4116558.
- Q4952019 wikiPageWikiLink Q41299.
- Q4952019 wikiPageWikiLink Q5062082.
- Q4952019 wikiPageWikiLink Q6159380.
- Q4952019 wikiPageWikiLink Q7200396.
- Q4952019 wikiPageWikiLink Q751484.
- Q4952019 wikiPageWikiLink Q7692636.
- Q4952019 wikiPageWikiLink Q957661.
- Q4952019 comment "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, usually coded as -1, 0, +1. (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.".
- Q4952019 label "Box–Behnken design".