How do I handle constraints (temperature/incubator space) in DOE

Question

Hello!

I am setting up a screening design for several (6) factors in a fermentation. The factors include temp, agitation, % sugar, yeast inoculation level, initial pH, and time at 2 levels per factor. The thought was to use a 2^5-1 factorial to achieve resolution with main and 2-level interaction effects. However, we have a constraint of only 1 incubator can be used, so only 1 temperature can be set at a time. Seeing as time of the fermentation ranges from 15-30 days, it would be ideal to only run 2 groups (low and high temp). It is not ideal to set temperature as a hard-to-change factor and have more than 2 whole plots.

Does anyone have any suggestions in this scenario? Would it be unadvisable to generate a completely randomized factorial and run it in 2 groups by temperature?

statman · Answer

Yes, there are 2 whole plots made by the temp low and high settings.  Make sure you separate this effect when analyzing the sub-plot (analyze the remaining factors interactions in the sub-plot with the normal/Pareto plots. You will get the temp.-factor interactions with increased precision).

You can always add center points.  Whether it is done automatically by a JMP selection or you just add multiple rows with center point coding (I recommend -1, 0, 1 for coding...always equidistant centered on 0).  If you do multiple center points, do them randomly throughout the experimentation and you will be able to get some idea of stability during the experiment.

For THE paper on split-plots, see Box and Jones "Split-plot designs for robust product experimentation", Journal of Applied Statistics, Vol. 19, No. 1, 1992

MRL255 · Answer

So you are saying to only have 2 whole plots (1 group of low temp and 1 group of high temp) and accept the very low power of temperature? Additionally, with the split plot method, it seems like JMP does not have the capability to add center points, is this true?

statman · Answer

There are options each with their own pros and cons.

You can do a split-plot design where temp is in the whole plot  and you don't do replicates.  While you will have no whole plot error as a basis for a statistical test, you can graphically evaluate the temperature effect to see whether it is of practical significance.  While you compromise information regarding the whole plot, you increase the precision of the sub-plot.