Why is it not a good idea to set continuous factor to zero for RSM

[#1]

Dear JMP-Experts,

I have quite often the case that continuous factor settings including a zero for lowest factor setting (0, 1, 2) are requested for liquid biotech formulation optimizations. These requests usually come people who are used to set up experiments with OFAT and it is not intuitve for them to understand, that setting factor to zero technical means to have a categorical factor setting.
Is there a better more practical why to explain this?

Thanks a lot in advance

[#2 · Accepted solution]

Hi @DualARIMACougar,

There is probably no definitive response to your question but here are some comments :

• DoE is most efficient when it relies on sequential iterations, when you first start by screening important main effects (with a screening design), and then augment it on the important factors to explore a little more higher order effects (interactions, quadratic effects), to finally create an optimization design in a narrower experimental space, with a focus on predictivity and process/product optimization.
  Depending on how you have conducted your first steps/designs and if/how you have reduced or expanded your experimental space of interest, the level 0 may be absent from the factors levels of your RSM, as factors seen as non-significant in previous steps may have already been filtered out, and other important factors may have a range of interest non-including 0 to reach an optimum. However, having a level at 0 in the initial steps/designs (screening) may be very interesting, as it enables to quickly remove non-important/significant factors from your system, as it will certainly highlight strong differences between presence and absence of the factor.
  So depending if you're doing optimization directly without prior designs/steps (because you have limited number of factors, so you can include level 0 to detect important effects and "map" the experimental space to do optimization) or rely on sequential experimentations, you may have at the end different ranges and design choices/augmentation.
  
  
• If you're talking about formulations optimization, you may be using mixture experiments. Structure of model-based mixture designs are very "logical" if you don't have specific constraints in your experimental space or factors, as it will create experiments with one factor, then binary blends, then ternary blends, etc... depending on the complexity of your assumed model. So you'll end up (without min constraints on the factors) with experiments having level 0 for your mixture factors. See the different design types and blends : Overview of Mixture Designs ; Examples of Mixture Design Types
  
  
• The problem definition (objective, factors & types, levels, responses, model, etc...) in DoE is the most important part and the one where domain expertise plays a vital role. Without knowledge from your use case, I can't assess if including 0 level is interesting or not. It's part of the objective you're trying to solve, as well as any practical constraints/consideration about the use and handling of your factors. However, be "bold" in the factors ranges, it's more often that a DoE doesn't deliver results due to too narrow factors ranges than due to too broad factors ranges. You can always reduce the experimental space in a design augmentation next to focus on the area of interest. 

If you're trying to convince colleagues that DoE is more effective than OFAT, try to find a study where they have done OFAT, create a DoE for the same topic with the same factors, and use the Compare Designs platform to highlight the gains : reduced number of experiments required, better power (so better evidence about the factors significance), reduced prediction variance over the experimental space, better handling of correlations/aliases between effects, ....

Hope these comments may help you,

[#3]

Hi Victor,

thanks for your answer. We want to measure the effect of factor variation in the course of a robustness study using three factor settings for each factor with the original condition in the middle. For one factor, 0 was requested as lowest factor setting, which is mathematical (for fitting the model later) valid, but physically the factor (chemical excipient) is absent in the condition. Previously I learned from experts on the community forum, that rather a low factor setting should be preferred instead of zero.

We dont have the capacity of running a screening design and than an optimization design after. Thats why we start from the beginning with RSM.

I hope this informations give a bit of an insight.

Thanks a lot