mixDesign: Mixture Designs

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 = 1234
)

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

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

total

Numeric 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

Nmerical value giving the input for set.seed.

Value

The function mixDesig() returns an object of class mixDesig().

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.

Examples

# Example usage of mixDesign
mdo <- mixDesign(3, 2, center = FALSE, axial = FALSE, randomize = FALSE, replicates = c(1, 1, 2, 3))

mdo$names(c("polyethylene", "polystyrene", "polypropylene"))
elongation <- c(11.0, 12.4, 15.0, 14.8, 16.1, 17.7,
                16.4, 16.6, 8.8, 10.0, 10.0, 9.7,
                11.8, 16.8, 16.0)
mdo$.response(elongation)

mdo$units()
#> $polyethylene
#> [1] "%"
#> 
#> $polystyrene
#> [1] "%"
#> 
#> $polypropylene
#> [1] "%"
#> 
mdo$summary()
#> Simplex LATTICE Design
#> Information about the factors:
#> 
#>      polyethylene polystyrene polypropylene
#> low             0           0             0
#> high            1           1             1
#> name polyethylene polystyrene polypropylene
#> unit            %           %             %
#> type      numeric     numeric       numeric
#> 
#> -----------
#> 
#> Information about the Design Points:
#> 
#>            1-blend 2-blend
#> Unique           3       3
#> Replicates       2       3
#> Sub Total        6       9
#> Total           15        
#> 
#> -----------
#> 
#> Information about the constraints:
#> 
#> A >= 0 B >= 0 C >= 0
#> 
#> -----------
#> 
#>                               PseudoComponent _|_ Proportion _|_ Amount
#> 
#>    StandOrder RunOrder    Type |   A   B   C _ | _   A   B   C _ | _   A   B
#> 1           1        1 1-blend | 1.0 0.0 0.0   |   1.0 0.0 0.0   |   1.0 0.0
#> 2           2        2 1-blend | 1.0 0.0 0.0   |   1.0 0.0 0.0   |   1.0 0.0
#> 3           3        3 2-blend | 0.5 0.5 0.0   |   0.5 0.5 0.0   |   0.5 0.5
#> 4           4        4 2-blend | 0.5 0.5 0.0   |   0.5 0.5 0.0   |   0.5 0.5
#> 5           5        5 2-blend | 0.5 0.5 0.0   |   0.5 0.5 0.0   |   0.5 0.5
#> 6           6        6 2-blend | 0.5 0.0 0.5   |   0.5 0.0 0.5   |   0.5 0.0
#> 7           7        7 2-blend | 0.5 0.0 0.5   |   0.5 0.0 0.5   |   0.5 0.0
#> 8           8        8 2-blend | 0.5 0.0 0.5   |   0.5 0.0 0.5   |   0.5 0.0
#> 9           9        9 1-blend | 0.0 1.0 0.0   |   0.0 1.0 0.0   |   0.0 1.0
#> 10         10       10 1-blend | 0.0 1.0 0.0   |   0.0 1.0 0.0   |   0.0 1.0
#> 11         11       11 2-blend | 0.0 0.5 0.5   |   0.0 0.5 0.5   |   0.0 0.5
#> 12         12       12 2-blend | 0.0 0.5 0.5   |   0.0 0.5 0.5   |   0.0 0.5
#> 13         13       13 2-blend | 0.0 0.5 0.5   |   0.0 0.5 0.5   |   0.0 0.5
#> 14         14       14 1-blend | 0.0 0.0 1.0   |   0.0 0.0 1.0   |   0.0 0.0
#> 15         15       15 1-blend | 0.0 0.0 1.0   |   0.0 0.0 1.0   |   0.0 0.0
#>      C | elongation
#> 1  0.0 |       11.0
#> 2  0.0 |       12.4
#> 3  0.0 |       15.0
#> 4  0.0 |       14.8
#> 5  0.0 |       16.1
#> 6  0.5 |       17.7
#> 7  0.5 |       16.4
#> 8  0.5 |       16.6
#> 9  0.0 |        8.8
#> 10 0.0 |       10.0
#> 11 0.5 |       10.0
#> 12 0.5 |        9.7
#> 13 0.5 |       11.8
#> 14 1.0 |       16.8
#> 15 1.0 |       16.0
#> 
#> -----------
#> 
#> Mixture Total: 1 equals 1
#>

Usage

Arguments

Value

Note

See also

Examples