DOE with 2 factors, one of which becomes irrelevant at some values of the other

Question

I am designing a custom design to test the effects of concentration and timing of addition of an additive on the yield of process.  I want to include adding none of the additive in the design.  How do I get around the absurdity of having timing of addition be a variable when nothing is added?  Is there a way to tell JMP to only make the timing variable relevant at concentrations greater than zero?

BigMig · Answer

Thanks.  My current strategy is to design the experiment with both factors but first analyze the data first with only concentration to find if adding the additive is even desirable.  If the analysis shows that then I would add the timing and do the analysis with both factors.  I know that this is not very elegant which is why I poster the question.

stephen_pearson · Answer

I would always urge cation when trying experiments where something is absent. In these circumstances your continuous variable become categorical (yes/no). If you consider your experimental budget you may like to take a two step approach. Firstly using a cheap design like a fractional factorial determine how much of a benefit the additive has. Secondly investigate the timing (and/or amount). This approach assumes you have some prior knowledge on a reasonable addition time.

gzmorgan0 · Answer

If I understand your problem this is called an experimental design with a negative control group. Drug studies call then placebo-controlled experimental designs, and industrial experiments call them "baseline" trials.

A 2 continuous factor DOE is usually interested in developing a predictive model or finding a path for the goal, improved yield (i.e. steepest ascent or interaction exploration).  However, a negative control group most often is used as a comparative group.

I suggest you design your 2-factor experiment, and how you "add" your negative control depends upon your DOE. For example suppose you have a blocking factor, like batch or lot or equipment, where you will be running the experiment on K blocks. Then you should add your negative control with each block.   If you are using replication, there should be some replication of the negative control.  And order should be randomized (if possible).

Since you are looking at no additive vs. different concentrations of additive, be very careful in planning your experiment so there is no bias introduced by contamination or accumulation effects.

Without more context, that is all I can recommend for designing your experiment.

Regarding analyses once the experimental results are available, here are a couple suggestions:

* Create a variability chart of  the raw results, yield vs. grouping factors, concentration and timing where the negative control will have  0 as the level for each factor.  If you have blocking factors, include those as grouping factors as well. This will help you look for outliers or other data anomalies, and start the comparison of the negative control (0,0) vs. other results.
* Analyze the 2-continuous factor experiment without the negative control: create the model, optimize etc.   
* Then, if needed, compare the yield (mean) and stability (if reps) of the negative control (baseline) with the proposed/modeled conditions. Sometimes, and ANOVA will be used, but often not necessary,

There might be others in the JMP Community with good examples, suggestions or references who have opposing or aditional suggestions.

I hope your experiment goes well and you learn much.