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- Box–Behnken_design 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.".
- Box–Behnken_design wikiPageExternalLink handbook.
- Box–Behnken_design wikiPageExternalLink pri3362.htm.
- Box–Behnken_design wikiPageExternalLink pri3363.htm.
- Box–Behnken_design wikiPageID "11086228".
- Box–Behnken_design wikiPageLength "4698".
- Box–Behnken_design wikiPageOutDegree "16".
- Box–Behnken_design wikiPageRevisionID "576402160".
- Box–Behnken_design wikiPageWikiLink Block_design.
- Box–Behnken_design wikiPageWikiLink Category:Design_of_experiments.
- Box–Behnken_design wikiPageWikiLink Central_composite_design.
- Box–Behnken_design wikiPageWikiLink Design_of_experiments.
- Box–Behnken_design wikiPageWikiLink Efficiency_(statistics).
- Box–Behnken_design wikiPageWikiLink Factorial_experiment.
- Box–Behnken_design wikiPageWikiLink General_linear_model.
- Box–Behnken_design wikiPageWikiLink George_E._P._Box.
- Box–Behnken_design wikiPageWikiLink National_Institute_of_Standards_and_Technology.
- Box–Behnken_design wikiPageWikiLink Plackett–Burman_design.
- Box–Behnken_design wikiPageWikiLink Quadratic_equation.
- Box–Behnken_design wikiPageWikiLink Response_surface_methodology.
- Box–Behnken_design wikiPageWikiLink Statistics.
- Box–Behnken_design wikiPageWikiLink Technometrics.
- Box–Behnken_design wikiPageWikiLinkText "Box–Behnken design".
- Box–Behnken_design wikiPageUsesTemplate Template:Experimental_design.
- Box–Behnken_design wikiPageUsesTemplate Template:Statistics.
- Box–Behnken_design subject Category:Design_of_experiments.
- Box–Behnken_design hypernym Designs.
- Box–Behnken_design type MeanOfTransportation.
- Box–Behnken_design type Page.
- Box–Behnken_design type Redirect.
- Box–Behnken_design 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.".
- Box–Behnken_design label "Box–Behnken design".
- Box–Behnken_design sameAs Q4952019.
- Box–Behnken_design sameAs m.02q_kgm.
- Box–Behnken_design sameAs Q4952019.
- Box–Behnken_design wasDerivedFrom Box–Behnken_design?oldid=576402160.
- Box–Behnken_design isPrimaryTopicOf Box–Behnken_design.