qualityTools (version 1.53)

mixDesign: Mixture Designs

Description

function to generate simplex lattice and simplex centroid mixture designs with optional center points and axial points.

Usage

mixDesign(p, n = 3, type = "lattice", center = TRUE, axial = FALSE, delta, 
          replicates = 1, lower, total = 1, randomize, seed)

Arguments

p

numerical value giving the amount of factors.

n

numerical value specifying the degree (ignored if type = centroid).

type

character string giving the type of design. type can be lattice or centroid (referencing to the first source under the section references]. By default type is set to lattice.

center

logical value specifying whether (optional) center points will be added. By default center is set to TRUE.

axial

logical value specifying whether (optional) axial points will be added. By default axial is set to FALSE.

delta

numerical value giving the delta (see references) for axial runs. No default setting.

replicates

vector with the number of replicates for the different design points i.e. c(center = 1, axial = 1, pureBlend = 1, BinaryBlend = 1, p-3 blend, p-2 blend, p-1 blend). By default replicates is set to 1.

lower

vector of lower-bound constraints on the component proportions (i.e. must be given in percent).

total

vector with

• [1] the percentage of the mixture made up by the q - components (e.g. q = 3 and x1 + x2 + x3 = 0.8 --> total = 0.8 with 0.2 for the other factors being held constant)
• [2] overall total in corresponding units (e.g. 200ml for t

randomize

logical value. If TRUE the RunOrder of the mixture design will be randomized (default).

seed

numerical value giving the input for set.seed.

Value

• mixDesig() returns an object of class mixDesign.

References

• CORNELL: Experiments with Mixtures - 3rd Ed. New Jersey: Wiley, 2011.
• CHASALOW, S. ; BRAND, R.: Generation of Simplex Lattice Points. Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 44, No. 4 (1995), pp. 534-545.

See Also

facDesign fracDesign rsmDesign wirePlot3 contourPlot3 http://www.r-qualitytools.org/Improve.html

Examples

#simplex lattice design with center (default response added with NA's)
mixDesign(p = 3, n = 2, center = FALSE)

#simplex lattice design with a center (default response added with NA's)
mixDesign(p = 3, n = 2, center = TRUE)

#simplex lattice design with augmented points (default response added with NA's)
mixDesign(p = 3, n = 2, center = FALSE, axial = TRUE)

#simplex lattice design with augmented points, center and 2 replications 
#(default response added with NA's)
mixDesign(p = 3, n = 2, center = TRUE, axial = TRUE, replicates = 2)

#simplex centroid design giving 2^(p-1) distinct design points 
#(default response added with NA's)
mixDesign(p = 3, n = 2, type = "centroid")

#simplex centroid design with augmented points (default response added with NA's)
mixDesign(p = 3, n = 2, type = "centroid", axial = TRUE)



#yarn elongation example from Cornell (2002)
mdo = mixDesign(3,2, center = FALSE, axial = FALSE, randomize = FALSE, 
                replicates  = c(1,1,2,3))
#set names (optional)
names(mdo) = c("polyethylene", "polystyrene", "polypropylene")
#units(mdo) = "\%" #set units (optional)
#set response (i.e. yarn elongation)
elongation = c(11.0, 12.4, 15.0, 14.8, 16.1, 17.7, 16.4, 16.6, 8.8, 10.0, 10.0,
               9.7, 11.8, 16.8, 16.0)  
response(mdo) = elongation

#print a summary of the design
summary(mdo)

#show contourPlot and wirePlot
dev.new(14, 14);par(mfrow = c(2,2))
contourPlot3(A, B, C, elongation, data = mdo, form = "quadratic")
wirePlot3(A, B, C, elongation, data = mdo, form = "quadratic", theta = 190)
wirePlot3(A, B, C, elongation, data = mdo, form = "quadratic", phi = 390, 
          theta = 0)
wirePlot3(A, B, C, elongation, data = mdo, form = "quadratic", phi = 90)