Questions regarding Response Surface Methodology (Box-Behnken design matrix)

[#1]

Good morning, 

I am currently trying to optimize some enzymatic reactions using Response Surface Methodology, in concrete, Box-Behnken design matrix. 

Using the program, you choose your independent variables or factors (pH, temperature, enzyme load, etc) and assign a "low" and "high" value to each. The program then automatically calculates the "middle" value. 

My first question is if it is possible to change that "middle" value. Mi low value for enzyme load is 5 U/mL and my high value, 20. So, the middle point should be 12,5 U/mL. However, I have conducted my "middle" reactions with 10 U/mL. The program allows you to change the suggested values very easily, so that's what I have done. Is there any problem with this? I assume that, given that the program allows these changes, it will optimize reaction conditions taking into account I have used the value of 10 instead of 12,5.

My next question is if I can add more reactions (with different combinations of the factors) than the ones suggested by the program. This is because I did some reactions before designing the experiment with the program and I have results ("responses") for reactions conducted at different combinations of the variables than those suggested by the program. I know design of experiments are meant to minimize the number of reactions needed for optimization of a process but, since I already have those values, I think they could be useful to make the prediction model stronger. 

Thank you very much in advanced.

Carlos

[#2]

You won't be thrown in DOE jail for putting the 'middle' values in a place that isn't in the middle of the factor space. This has a bit of a 'harmful', and that's probably too strong a word to use, on the orthogonality of the design...but it's generally not a fatal consequence.

Adding additional runs to the design space is very doable in JMP from a procedural point of view...but has some assumptions that should go along with it...like the presence or absence of nuisance/noise variables and their effects between the core design and the additional runs. What does your gut tell you about this...for example, in the core design maybe you are using one supplier's materials...and in the other runs, you used a different supplier. Are you willing to assume there is no effect due to supplier material differences?

These additional runs will also further influence the correlation of the effects in the core design and might make for some correlations among estimates that you didn't anticipate. So before proceeding with analysis you might want to use the Compare Designs platform to evaluate the effect of adding these runs...on the plus size, all other things being equal, the power of your merged design should increase.

[#3]

Pete's advice is right on.  I have some additional thoughts...completely my humble opinion, so you may want to ignore it.

1. Designed experiments are intended to provide an effective and often an efficient means of understanding causal relationships between independent variables and dependent variables.  Once you have determined that you have a robust model (meaning you have experimented over changing noise conditions and the results are consistent), you may choose to further understand the response surface.  This can be done in one design that will provide sufficient "filling" of the design space, or in sequential deigns that are "additive" (Box approach).  The Box Behnken design is particularly useful for factors that can't be run at their extremes, so the extremes are excluded from the design.

2.  Not sure why you don't simply put the - and + equidistant from the center point of 10 ( 5 and 15)?  Balanced designs are easier to analyze and perhaps less biased.  But do what makes most sense to you.

3. Pete is correct, it does no good to develop a complex model that worked yesterday, but not tomorrow.

4.  I would think in terms of a complex surface you are trying to map.  That's  how I would analyze it as well.  You already know statistical significance (and should have a first order model), so now you're fine tuning.  Complexity isn't necessarily a good thing, though it may be cool.  The model has to be manageable.