bbdesign

R2026b

Box-Behnken design

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Syntax

dBB = bbdesign(n)
dBB = bbdesign(n,Name=Value)
[dBB,blocks] = bbdesign(___)

Description

dBB = bbdesign(n) returns a numeric matrix dBB containing a Box-Behnken design for n factors, where n is a positive integer scalar greater than or equal to 3. The size of dBB is m-by-n, where m is the number of runs (points) in the design. Each row of dBB contains the settings for all factors in a run, scaled between –1 and 1.

dBB = bbdesign(n,Name=Value) returns dBB with additional options specified by one or more name-value arguments. For example, you can specify the number of center points, and the maximum number of points per block.

example

[dBB,blocks] = bbdesign(___) additionally returns a 1-by-m vector containing the block numbers for each run, using any of the input argument combinations in the previous syntaxes. The blocks indicate the runs to measure under similar conditions in order to minimize the effect of inter-block differences on the parameter estimates.

Examples

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Open Live Script

Create a three-factor Box-Behnken design with four center points.

dBB = bbdesign(3,Center=4);

Display the last five runs of the design.

disp(dBB(end-4:end,:))
     0     1     1
     0     0     0
     0     0     0
     0     0     0
     0     0     0

The design contains four center points for a more uniform estimate of the prediction variance over the entire design space.

Visualize the design using the plot3 function.

plot3(dBB(:,1),dBB(:,2),dBB(:,3),"ro", ...
         MarkerFaceColor="b")
set(gca,Box="on",BoxStyle="full")
axis square equal

Figure contains an axes object. The axes contains a line object which displays its values using only markers.

The coordinates of each marked point in the cube represent the factor settings of a run in the design.

Input Arguments

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Number of factors in the design, specified as a positive integer scalar greater than or equal to 3.

Example: 3

Data Types: single | double

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: bbdesign(3,Center=2) creates a Box-Behnken design for three factors that contains two center points.

Number of center points in the design, specified as a nonnegative integer. The default value depends on n.

Example: Center=3

Data Types: single | double

Maximum number of points per block, specified as a positive integer. The default value is Inf.

Example: BlockSize=3

Data Types: single | double

Output Arguments

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Box-Behnken design for n factors, returned as a numeric matrix of size m-by-n, where m is the number of runs (points) in the design. Each row of dBB contains the settings for all factors in a run, scaled between –1 and 1.

Block numbers for each run (point), returned as an m-by-1 numeric vector, where m is the number of runs in the design. The blocks indicate the runs to measure under similar conditions in order to minimize the effect of inter-block differences on the parameter estimates. For more information, see [1].

Alternative Functionality

Instead of using bbdesign, you can create a responseSurfaceDOE object by using the responseSurfaceDOE function. The responseSurfaceDOE function provides the following advantages:

  • The function allows you to specify design options such as the factor names, factor level bounds, blocks, and experiment model.

  • In addition to returning the design runs, the function stores your specifications in the responseSurfaceDOE object properties.

  • After you create a responseSurfaceDOE object, you can:

    • Fit a linear regression model to the design run responses using the fitlm function.

    • Randomize the run order in the design using the randomizeRunOrder function.

    • Add replicates (duplicates of the original design runs) using the addReplicates function.

References

[1] Box, G. E. P., W. G. Hunter, and J. S. Hunter. Statistics for Experimenters. Hoboken, NJ: Wiley-Interscience, 1978.

[2] Box, G. E. P., and D. Behnken. "Some New Three Level Designs for the Study of Quantitative Variables." Technometrics 2, no. 4 (November 1960): 455–75.

Version History

Introduced before R2006a

See Also

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