I have results from two DoEs, the first one includes 4 factors:
| Variable | Levels |
| -------- | -------------- |
| x1 | 0.9, 2.1, 2.9 |
| x2 | 1.64, 2.16 |
| x3 | 0.8, 1.15, 1.5 |
| x4 | 7, 7.5, 8 |
nruns = 18
After the experiment, we record the response: y. Through rsm, we conclude that maximum y is achieved by:
| Variable | |
| -------- | ---- |
| x1 | 0.9 |
| x2 | 1.64 |
| x3 | 0.8 |
| x4 | 8 |
We intend to explore the levels of x3 and x4 beyond the ones we already tried (in hope to increase y even more than the current maximum). So a second DoE is made:
| Variable | Levels |
| -------- | -------------- |
| x1 | 0.9 |
| x2 | 1.64 |
| x3 | 0, 0.5, 1, 1.5 |
| x4 | 8, 8.5, 9, 9.5 |
nruns = 16
Is it wise to compile data from both DoE and create a new y model?
I have tried modeling the first DoE result:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.6125 3.3328 16.0865 1.782e-08 ***
x1 -8.1076 2.4799 -3.2693 0.0084402 **
x2 -15.5089 2.2637 -6.8512 4.452e-05 ***
x3 -18.9195 2.3624 -8.0085 1.167e-05 ***
x4 12.9776 2.4584 5.2789 0.0003582 ***
x1:x3 6.1652 3.0419 2.0268 0.0701846 .
x3:x4 -13.1467 3.5887 -3.6634 0.0043646 **
x3^2 -8.3503 4.0768 -2.0483 0.0677031 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Multiple R-squared: 0.9373, Adjusted R-squared: 0.8934
F-statistic: 21.35 on 7 and 10 DF, p-value: 2.989e-05
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
FO(x1, x2, x3, x4) 4 8250.9 2062.72 31.0278 1.297e-05
TWI(x1, x3) 1 511.2 511.22 7.6898 0.019684
TWI(x3, x4) 1 892.2 892.18 13.4203 0.004365
PQ(x3) 1 278.9 278.91 4.1954 0.067703
Residuals 10 664.8 66.48
Lack of fit 10 664.8 66.48 NaN NaN
Pure error 0 0.0 NaN
Stationary point of response surface:
x1 x2 x3 x4
1.064145 0.000000 1.046257 -2.269172
Stationary point in original units:
x1 x2 x3 x4
2.964145 1.900000 1.516190 6.365414
Eigenanalysis:
eigen() decomposition
$values
[1] 4.199982 0.000000 0.000000 -12.550315
$vectors
[,1] [,2] [,3] [,4]
x1 0.3675223 9.053867e-01 0 0.2126082
x2 0.0000000 0.000000e+00 1 0.0000000
x3 0.5007402 3.442183e-16 0 -0.8655976
x4 -0.7837006 4.245879e-01 0 -0.4533635
and tried modeling the compiled data:
dfcoded <- coded.data(df2,
x1 ~ (2*(x1 - 0.9)/2) - 1,
x2 ~ (2*(x2 - 1.64)/0.52) - 1,
x3 ~ (2*(x3 - 0)/1.5) - 1,
x4 ~ (2*(x4 - 7)/2.5) - 1)
m <- rsm(Binding ~
FO(x1, x2, x3, x4) +
TWI(x1, x4) +
TWI(x2, x3) + TWI(x2, x4) +
PQ(x3),
data = dfcoded)
summary(m) # best
Estimate Std. Error t value Pr(>|t|)
(Intercept) 66.3728 4.8140 13.7874 3.466e-13 ***
x1 6.9777 5.1197 1.3629 0.185060
x2 10.6011 5.0716 2.0903 0.046920 *
x3 -12.7635 6.7357 -1.8949 0.069726 .
x4 11.0079 7.5260 1.4627 0.156021
x1:x4 19.1074 7.4883 2.5516 0.017217 *
x2:x3 -22.7937 6.4498 -3.5340 0.001621 **
x2:x4 15.3252 7.7275 1.9832 0.058431 .
x3^2 -12.8778 5.2347 -2.4601 0.021152 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Multiple R-squared: 0.8106, Adjusted R-squared: 0.75
F-statistic: 13.37 on 8 and 25 DF, p-value: 2.634e-07
Analysis of Variance Table
Response: y
Df Sum Sq Mean Sq F value Pr(>F)
FO(x1, x2, x3, x4) 4 2976.7 744.2 5.9408 0.001674
TWI(x1, x4) 1 4231.7 4231.7 33.7825 4.638e-06
TWI(x2, x3) 1 4978.5 4978.5 39.7437 1.347e-06
TWI(x2, x4) 1 456.8 456.8 3.6463 0.067734
PQ(x3) 1 758.1 758.1 6.0519 0.021152
Residuals 25 3131.6 125.3
Lack of fit 24 2986.4 124.4 0.8569 0.709247
Pure error 1 145.2 145.2
Stationary point of response surface:
x1 x2 x3 x4
0.07199339 -0.80804612 0.21955856 -0.36518518
Stationary point in original units:
x1 x2 x3 x4
1.9719934 1.6899080 0.9146689 7.7935185
Eigenanalysis:
eigen() decomposition
$values
[1] 13.544086 4.221524 -10.086293 -20.557069
$vectors
[,1] [,2] [,3] [,4]
x1 -0.4522197 -0.6143887 0.63559781 -0.1184878
x2 -0.5693598 0.6164495 0.09081844 -0.5362568
x3 0.2455887 -0.4108699 -0.37078955 -0.7958563
x4 -0.6411029 -0.2714821 -0.67103096 0.2549549