Generate a Response Surface Design
DESCRIPTION:
Generates a design data frame which can be used to fit response surfaces to data.
USAGE: 
rsm.design(n.factors, factor.names.arg =
     std.factor.names(n.factors),type = "cc", n.cp =
     min( n.factors + 1, 4), alpha, logx = F, fraction)
REQUIRED ARGUMENTS:
n.factors:
An integer for the number of factors in the design.
OPTIONAL ARGUMENTS:
factor.names.arg:
Either a vector of names for the factors or a list. If a list, the names of the list give the factors names. If type is "cc", "fc" or "bb", each element of the list gives two numbers, specifying the "cube" points of each factor, i.e., the "Low" and "High" points ( See details below.). The default levels are c(-1,1) for natural scale and c(.01, 10) for log scale. If type is "3^n", each element gives three numbers, specifying the three levels of each factor. The default levels are c(-1,0,1) for natural scale and c(.01, 1, 10) for log scale.
type:
Character string for type of response surface design. Valid types are: "cc" = central composite, "fc" = face centered cube, "3^n" = factorial design with three levels per factor, and "bb" = Box Behnkens design.
n.cp:
the number of center points in the design. Default is min(number of factors + 1,4).
alpha:
scalar or vector of alpha values for the factors. If a scalar, the same value used for all factors. If a vector, its length must equal the number of factors. Default is 2^(nc/4), where nc is the number of points in the cube, or fractional factorial part of the design.
logx:
A vector of logical values indicating whether a variable is to be "equally spaced" on the log rather than the natural scale. If logx, has length 1, the same value is used for all factors.
fraction:
number giving the fraction desired for the cube design. This allows selection of a fraction of the full factorial design for the cube, reducing the total number of runs. By default a resolution V design is used. This argument only applies to central composite designs.
VALUE:
returns a design data frame of class rsm.design which inherits from design and data.frame. Each of the factors in the returned design has class rsm.factor. See documentation of rsm.factor object for a discussion of their attributes.
DETAILS:
A central composite design has three components: the "cube" (a fractional factorial design on the Low and High points), center points (in the center of the cube), and star points (points extended from the center of each face of the cube).

Each factor in the returned design has five values: Low Star, Low, Center, High and High Star. Low and High are given in the factor.names.arg list, if supplied. They default to -1 and 1. Center is the average of Low and High. Low Star = Center - alpha * (High -Low) * 0.5; Hi Star = Center - alpha * (Hi - Low) * 0.5

A face centered design is a central composite design with alpha = 1. This means each factor only has three levels, rather than the five of the general central composite design.

The factorial design with three levels per factor, is a full factorial design, and typically requires a large number of runs (3^n, where n is the number of factors)

Box-Behnken designs are designs with only three levels per factor that are economical in the number of runs required. In S+DOX, these are available for up to 7 factors.

REFERENCES:
Box, G.E.P. and Draper, N.R (1987), Empirical Model Building and Response Surfaces, New York: Wiley.

Haaland, P.D. (1989), Experimental Design in Biotechnology, New York: Marcel Dekker.

SEE ALSO:
rsm.lm , as.rsm.factor , rsm.factor , design.design , fac.design, summary.rsm.design , print.rsm.design
EXAMPLES: 
# generate a central composite design
rsm.design(2,list(RadDos=c(100,300),Prime1=c(7,21)))


# generate a central composite design with factors on
# a log scale
rsm.design(2,list(A=c(2,8),B=c(1,100)),log=c(T,T))


# generate a central composite design which has as its
# base fraction a resolution IV design rather than the
# default resolution V design
rsm.design(7, fraction = 1/8)


# generate a factorial design with 3 factors each at 3 levels
rsm.design(3, n.cp = 3, type= "3^n")


# generate a Box-Behnken design with the first two
# factors on a log scale
rsm.design(6, type = "bb", log = c(T,T,F,F,F,F))


# generate a face centered design
rsm.design(3,alpha=1)