DoE.multi.response
The goal of DoE.multi.response is to construct experimental designs that follow the structure of well studied designs (such as CCDs), but extended to problems with multiple response variables where there is some prior information about the relationship between explanatory and response variables.
Example
This is a basic example which shows you how to solve a common problem:
We have a system with four response variables and 5 explanatory variables (factors). Suppose we know from previous process knowledge that:
- Response 1 is related to factors 1, 2, and 3
- Response 2 is related to factors 2, 3, and 4
- Response 3 is related to factors 1, 3, and 5
- Response 4 is related to factors 1 and 4
We can summarize this prior information with the following table:
| factors | f1 | f2 | f3 | f4 | f5 |
|---|---|---|---|---|---|
| Response 1 | X | X | X | ||
| Response 2 | X | X | X | ||
| Response 3 | X | X | X | ||
| Response 4 | X | X |
One assignment of unique factors for this example is:
x<-matrix(c(1,1,1,0,0,
0,1,1,1,0,
1,0,1,0,1,
1,0,0,1,0), nrow = 4,byrow = TRUE)
library(DoE.multi.response)
#> Loading required package: DoE.wrapper
#> Loading required package: FrF2
#> Loading required package: DoE.base
#> Loading required package: grid
#> Loading required package: conf.design
#>
#> Attaching package: 'DoE.base'
#> The following objects are masked from 'package:stats':
#>
#> aov, lm
#> The following object is masked from 'package:graphics':
#>
#> plot.design
#> The following object is masked from 'package:base':
#>
#> lengths
#> Loading required package: rsm
ufactors(x)
#> [1] 1 2 3 4 2And a UF-CCD for this example is:
ufccd(x)
#> full factorial design needed
#> creating full factorial with 16 runs ...
#> Block.ccd X1 X2 X3 X4 X5
#> C1.17 1 0.00000 0.00000 0.00000 0.00000 0.00000
#> C1.18 1 0.00000 0.00000 0.00000 0.00000 0.00000
#> C1.13 1 -1.00000 -1.00000 1.00000 1.00000 -1.00000
#> C1.14 1 1.00000 -1.00000 1.00000 1.00000 -1.00000
#> C1.1 1 -1.00000 -1.00000 -1.00000 -1.00000 -1.00000
#> C1.16 1 1.00000 1.00000 1.00000 1.00000 1.00000
#> C1.15 1 -1.00000 1.00000 1.00000 1.00000 1.00000
#> C1.8 1 1.00000 1.00000 1.00000 -1.00000 1.00000
#> C1.9 1 -1.00000 -1.00000 -1.00000 1.00000 -1.00000
#> C1.5 1 -1.00000 -1.00000 1.00000 -1.00000 -1.00000
#> C1.19 1 0.00000 0.00000 0.00000 0.00000 0.00000
#> C1.6 1 1.00000 -1.00000 1.00000 -1.00000 -1.00000
#> C1.2 1 1.00000 -1.00000 -1.00000 -1.00000 -1.00000
#> C1.3 1 -1.00000 1.00000 -1.00000 -1.00000 1.00000
#> C1.11 1 -1.00000 1.00000 -1.00000 1.00000 1.00000
#> C1.7 1 -1.00000 1.00000 1.00000 -1.00000 1.00000
#> C1.10 1 1.00000 -1.00000 -1.00000 1.00000 -1.00000
#> C1.4 1 1.00000 1.00000 -1.00000 -1.00000 1.00000
#> C1.12 1 1.00000 1.00000 -1.00000 1.00000 1.00000
#> C1.20 1 0.00000 0.00000 0.00000 0.00000 0.00000
#> S2.9 2 0.00000 0.00000 0.00000 0.00000 0.00000
#> S2.6 2 0.00000 0.00000 2.19089 0.00000 0.00000
#> S2.8 2 0.00000 0.00000 0.00000 2.19089 0.00000
#> S2.7 2 0.00000 0.00000 0.00000 -2.19089 0.00000
#> S2.12 2 0.00000 0.00000 0.00000 0.00000 0.00000
#> S2.1 2 -2.19089 0.00000 0.00000 0.00000 0.00000
#> S2.10 2 0.00000 0.00000 0.00000 0.00000 0.00000
#> S2.5 2 0.00000 0.00000 -2.19089 0.00000 0.00000
#> S2.2 2 2.19089 0.00000 0.00000 0.00000 0.00000
#> S2.4 2 0.00000 2.19089 0.00000 0.00000 2.19089
#> S2.11 2 0.00000 0.00000 0.00000 0.00000 0.00000
#> S2.3 2 0.00000 -2.19089 0.00000 0.00000 -2.19089