# 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

 ```1 2``` ```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  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)  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 thomas.roth@tu-berlin.de

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```#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.