qualityTools (version 1.31.1)

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

number of factors

n

the degree (ignored if type = "centroid")

type

lattice or centroid

center

TRUE or FALSE for adding center points

axial

TRUE or FALSE for adding axial points

delta

delta for axial runs

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)

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 mixt

randomize

TRUE or FALSE, if TRUE the RunOrder of the mixture design will be randomized

seed

seed for randomization

Value

• an object of class mixDesign

References

Cornell (2002). Experiments with Mixtures. Third Edition. Wiley. Chasalow, S; Brand, R (1995) 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

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))
names(mdo) = c("polyethylene", "polystyrene", "polypropylene")#set names (optional)
#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)