In our study, we have completely randomized design with 3 replications and 30 seedling pretreatment was employed in the experiment. To see the effect of 3 different light qualities on the growth parameters, photosynthesis pigments, and phytochemical accumulations. In this study, the "on-factor-at-a-time" approach was employed to screen the main factors.
As we know that the conventional multivariable optimization is usually based on the " one-factor-at-a-time" approach, which is unable to detect interactions among independent variables.
How can we solve the drawbacks on the "one-factor-at-a-time" approach ??
I am not sure, if I completely understood your task, but from statistical point of view - why don´t you employ Design of Experiment (e.g. factorial designs) instead of the OFAT approach which you described? Even a screening (low and high settings plus center points) reveals interactions, a few more points in between will allow the determination of quadratic terms. Programs to set it up and for evaluation are e.g. MODDE from Umetrics or Design Expert.
The OFAT approach might be useful if the real problem is that you have too few experimental units to do anything more. In which case consider things like incomplete block designs and fractional replication. There are problems with these designs, and I strongly suggest consulting with a statistician before embarking on this adventure. If you have sufficient experimental material, then go with a factorial design.
Multivariate analysis is not predicated on the one factor at a time approach. Multiple regression, MANOVA, Factor analysis, etc... do not work well with testing one factor at a time.
If this does not help, please explain the rationale for using the OFAT approach, and provide a little more detail on the experiments that you are running. The more information that you are able to provide, the better chance we have in providing good suggestions.
Marek's idea of using Design Expert suggests a mixture design. The total might be the total energy or the total number of photons. I can see this working.
How many factors are you testing?
How many levels are there for each factor?
Are you able to control all of those factors?
You can use one or more of the classical design methods used by RA Fisher at Rothamsted. Factorial Designs, Split Plots, etc.
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