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)
#>
#> 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
ufactors(x)
#> [1] 1 2 3 4 2``````

And 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``````