Response Surface Design - How to "fool" JUMP ?

enaid

Hello,

I have a singular question. I would like to realize a response surface design on JUMP. I have two responses :

-         - Density of bread: I have to match the range 0.2 (minimum) to 0.3 (maximum);

          - Percentage of proteins: I have to maximize it.

I add an importance of 0.5 for each because the density is as important as the proteins content (I can’t reach one parameter without taking care about the other parameter).

I have 4 continuous factors which correspond to 4 flour varieties:

-        - Flour A : I have the results of experiments with no Flour A in the recipe, and with 100% of Flour A

         - Flour B  : I have the results of experiments with no Flour B in the recipe, and with 100% of Flour B

         - Flour C  : I have the results of experiments with no Flour C in the recipe, and with 100% of Flour C

         - Flour D : I have the results of experiments with no Flour D in the recipe, and with 100% of Flour D

        I want to know what is the best blend of flours that will permit me to reach the optimum density and maximize the proteins content ?

         

        My problem is that I don't have the experimental results for intermediaire percentages of flours in the recipe (and I could not obtain it anyway). I just have this incomplete plan :

Flour A	Flour B	Flour C	Flour D	Density	Proteins content (%)
1	0	0	0	x1	y1
0	1	0	0	x2	y2
0	0	1	0	x3	y3
0	0	0	1	x4	y4

I know that the effects of the flours are additionnal so I will have linear interaction between the four flours without any other interaction. However, I don't know how can I "fool" JUMP to do a response surface design with this incomplete table ? (Because obviously, JUMP ask me to do several runs with central points too). Is it possible to do a response surface design with this work ? In this case, is there an option in JUMP to avoid doing the other runs ?

I hope that the explanations are clear enough

Thank a lot for your help/remarks.

louv

This is a Mixture Design. Your ingredients are not undergoing a change but rather you are looking for a formulation or blend that co-optimizes your two responses of interest. There are various approaches to your problem. If you set up your design as a mixture design you will get the response surface design since the factors or variables are not independent. I would argue that 4 runs is a stretch and you should consider the ABCD Mixture design for 4 factors which would require 15 runs. However if that run number is excessive then consider the default number of runs for an optimal design which would be 10 runs. The bare minimum is 4 runs but that does not give you nay understanding of your error.