Determination of variables for optimizing one response using the desirability function

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Determination of variables for optimizing one response using the desirability function

Thanh Tran
Dear all,



I'm trying to use response surface methodology (rsm package) to . In my
data, the response is KIC, and 4 factors are AC, AV, T, and Temp. A typical
second-degree response modeling is as follows:



> data<-read.csv("2.csv", header =T)

> library(rsm)

> f.quad <- rsm(KIC~SO(AC, AV, T, Temp), data = data)

> summary(f.quad)



I summary the results as follows:



KIC = 4.85 – 2.9AC +0.151 AV + 0.1094T

          + 0.0091Temp + 0.324 AC^2-0.0156AV^2

          - 10.00106T^2 - 0.0009Temp^2 + 0.0071AC´AV

          - 0.00087AC´T -0.00083AC´Temp – 0.0018AV´T

         +0.0015AV´Temp – 0.000374 AV ´ T



Stationary point of response surface:

       AC        AV          T                Temp

 4.502353|  2.753002 | 48.278146 | -4.246307



Eigenanalysis:

eigen() decomposition

$`values`

[1]  0.324323665 -0.000736292 -0.001210406 -0.015776132



Based on the above response modeling and ranges of the factors (4<AC<5;
4<AV<7; 30<T<50; 5<Temp<25), I want to determine levels of the AC, AV, T,
and Temp to have the Maximum value of KIC. Because the stationary point is
an outside region of experiments, I try the desirability packages in R, but
it does not work because these packages almost focus on different responses
rather than variables.



I believe that there is a package which can solve this problem because,
with Minitab, the result using the desirability function can be shown in
Figure 1.



If anyone has any experience practicing the desirability function or
suggests any potential package, I appreciate your support and help.



Best regards,

Nhat Tran



Ps: I also added a CSV file for practicing R.
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