mixDesign: Mixture Designs

In qualityTools: Statistical Methods for Quality Science

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 the overall mixture)
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.

Note

In this version the creation of (augmented) lattice, centroid mixture designs is fully supported. Getters and Setter methods for the mixDesign object exist just as for objects of class facDesign (i.e. factorial designs).
The creation of constrained component proportions is partially supported but don't rely on it. Visualization (i.e. ternary plots) for some of these designs can be done with the help of the wirePlot3 and contourPlot3 function.
Visualization is however BETA and the analysis of mixture designs is not as convenvient as for objects of class facDesign (i.e. needs to be done manually, at this point). Feedback is welcome...

For an example in context which shows the usage of the function mixDesign() to an object of class facDesign, please read the vignette for the package qualityTools at http://www.r-qualitytools.org/html/Improve.html.

Author(s)

Thomas Roth [e-mail]

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/html/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)

qualityTools documentation built on May 2, 2019, 10:21 a.m.