5. • Help you better understand and optimize your
response.
• Used to refine models after you have determined
important factors using factorial designs
Advantages of Response surface design
6. Factorial Points : Estimated main factor & interaction
Axial Points : Estimated pure quadratic form
Center Points : Estimated pure Error
→ Building a quadratic response surface
→ Resolves both main effects and interactions
Central composite design (CCD)
14. 14
Model is fixed
Algebra equation
Time-consuming
Model reduction
SAS regression
Interaction effect
Save time
0.00 0.25 0.50 0.75 1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
IBr
Cl
Binary Design (A) Ternary Design (B)
Modified mixture design methods
15. Advantages of mixture design
• Designs for these experiments are useful
because many product design and development
activities in industrial situations involve
formulations or mixtures.
23. Contour plot- e.g. PCE
A=tril(meshgrid(0:0.001:1));
B=tril(meshgrid(1:-0.001:0)');
C=tril(1-A-B);
x=tril(0.5.*(1+C-B));
y=tril((3^0.5)*0.5.*A);
z=5.57799.*A +4.53861.*B+6.53751.*C -5.83005.*A.*B
+64.07944.*A.*B.*C+11.75880.*B.*C.*(B-C);
[C,h] = contourf(x,y,z,
[1,2,3,4,5,6,6.5,7,7.2,7.4,7.6],'LineWidth',1);
axis([0,1,0,1]);
clabel(C,h,'manual','fontsize',15);
hold on
plot([0.375,0.625],[0.6495,0.6495],'k:');
hold on
plot([0.25,0.75],[0.433,0.433],'k:');
hold on
plot([0.375,0.75],[0.6495,0],'k:');
hold on
plot([0.25,0.5],[0.433,0],'k:');
hold on
plot([0.125,0.25],[0.2165,0],'k:');
hold on
plot([0.125,0.875],[0.2165,0.2165],'k:');
hold on
plot([0.25,0.625],[0,0.6495],'k:');
hold on
plot([0.50,0.75],[0,0.433],'k:');
hold on
plot([0.75,0.875],[0,0.2165],'k:');
先建立矩
陣數列,
從0~1,
間格0.001
利用SAS迴歸得到的Eq.
29. Factors and levels for the 23 Full Factorial Design
factors
levels
+ -
A, P3HT:PCBM concentration
(wt%)
2.5 1.5
B, rpm 600 1000
C, time (s) 60 40
Full Factorial Design