# [R] D-optimum design - optimization model

Thanh Tran m@@ternh@ttt @ending from gm@il@com
Mon Dec 3 14:03:33 CET 2018

```Dear all,

I'm trying to use the D-optimum design. 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:

> mod <- lm(KIC~AC+I(AC^2)+AV+I(AV^2)+T+I(T^2)+Temp+I(Temp^2)+AC:AV+AC:T+AC:Temp+AV:T+AV:Temp+T:Temp,

+ data = data)

The result of the model:

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

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

Based on the above response modelling, I want to determine levels of the
AC, AV, T, and Temp to have the Maximum value of KIC. The result running in
Minitab as is shown in Figure 1. In R, I try to compute an D-optimum design
with the following codes:

> attach(data)

> F.trig <- F.cube

> F.trip <-
F.cube(KIC~AC+I(AC^2)+AV+I(AV^2)+T+I(T^2)+Temp+I(Temp^2)+AC:AV+AC:T+AC:Temp+AV:T+AV:Temp+T:Temp,

+ c(4,4,30,5), # Smalesst values of AC,AV,T, and Temp

+ c(5,7,50,25), # Highest values of AC,AV,T, and Temp

+ c(3,3,3,3)) # Numbers of levels ofAC,AV,T, and Temp

> res.trip.D <- od.AA(F.trip,1,alg = "doom", crit = "D",

+ graph =1:7, t.max = 4)

I have the result as shown in Figure 2 but I cannot find out the optimum
design as shown in Figure 1 using Minitab.

If anyone has any experience about what would be the reason for error or
how I can solve it? I really appreciate your support and help.

Best regards,

Nhat Tran

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

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