Generates Box-Behnken designs (R.W. Payne).
Options
PRINT = string token |
Controls printed output (design); if unset in an interactive run AGBOXBEHNKEN will ask whether the design is to be printed, in a batch run the default is not to print anything |
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NCENTRALPOINTS = scalar |
Defines the number of central points to include; default 4 |
LEVELS = variate |
Defines the outer levels to be used; default !(-1,1) |
NCOMBINATIONS = scalar |
Number of factors to vary in combination at once; default 2 |
SEED = scalar |
Seed to be used to randomize each design; a negative value implies no randomization |
STATEMENT = text |
Saves a command to recreate the design (useful if the design information has been specified in response to questions from AGBOXBEHNKEN) |
Parameter
TREATMENTFACTOR = factors |
Treatment factors |
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Description
Box-Behnken designs are often used to study response surfaces. The design is usually formed to allow a quadratic response surface to be fitted. The factors are studied at three equally-spaced levels, below denoted by -1, 0 and 1. The construction uses a balanced incomplete block design to select successive sets of factors to be applied at all factorial combinations of -1 and +1, while other factors are held at 0. For example, with three factors A, B and C, the relevant balanced incomplete block design would have three blocks (A,B), (A,C) and (B,C). So the design would first have a section with A and B varying but C constant
A B C
-1 -1 0
-1 +1 0
+1 -1 0
+1 +1 0
then a section where B is held constant but A and C take all combinations of -1 and +1
A B C
-1 0 -1
-1 0 +1
+1 0 -1
+1 0 +1
and finally a section with A constant
A B C
0 -1 -1
0 -1 +1
0 +1 -1
0 +1 +1
In addition, there can be some “central points”, where all the factors take the central value
A B C
0 0 0
0 0 0
0 0 0
0 0 0
The treatment factors are listed using the TREATMENTFACTOR parameter. If this is omitted in an interactive run, you will be asked how many factors you want and their names. The number of central points is specified by the NCENTRALPOINTS option; by default this is taken to be four. The LEVELS option can supply a variate to specify the outer treatment levels; the defaults are 1 and -1 (so the central point is at zero). The NCOMBINATIONS option defines the number of factors whose combinations of (outer) levels are to be varied at once. For the default of two, the relevant balanced incomplete block design is formed within AGBOXBEHNKEN. Other values can be supplied, but the corresponding balanced incomplete block design must be one of those obtainable from procedure AGBIB. You can find out the possibilities by putting
AGBIB [PRINT=catalogue]
The SEED parameter allows you to specify a seed to be used to randomize the design. In batch the default seed is -1, to suppress randomization. If you do not set SEED when running interactively AGBOXBEHNKEN will ask for a seed, and again a negative value suppresses any randomization. The PRINT option can be set to design to print the plan of the design. By default, if you are running Genstat in batch, the plan is not printed. If you do not set PRINT when running interactively, AGBOXBEHNKEN will ask whether or not you wish to print the design.
The STATEMENT option allows you to save a Genstat text structure containing a command to recreate the design. This is particularly useful if AGBOXBEHNKEN is being used interactively, and the information to define the design has been provided in response to questions from the procedure.
Options: PRINT, NCENTRALPOINTS, LEVELS, NCOMBINATIONS, SEED, STATEMENT.
Parameter: TREATMENTFACTOR.
Method
The QUESTION procedure is used to obtain the necessary details of the design and this is then generated by the standard Genstat manipulation directives and procedure AGBIB.
See also
Directive: AFRESPONSESURFACE.
Procedures: AFNONLINEAR, AGCENTRALCOMPOSITE, AGMAINEFFECT, RQUADRATIC.
Commands for: Design of experiments, Regression analysis.
Example
CAPTION 'AGBOXBEHNKEN example'; STYLE=meta AGBOXBEHNKEN [PRINT=design] A,B,C,D