DOE Question: Contraints on Categorical Factors

Question

I would appreciate some advice...  I am running a screening experiment with strictly categorical factors and trying to identify the primary source of variation in my response.  The experiment involves material going into a surface process (known significant effect), followed by a bake (which needs to be done in batches to process everything through - any oven run to oven run variation?), followed by an assembly process (unknown impact, since always previously confounded with surface process).  The bake is the tricky bit that I'm having issues with in the design.  There are four positions in the oven (font/back, top/bottom), and in a previous experiment it looked like front vs back mattered, so I'd like keep oven location in the model as well.  Experimental units: 40.  Surface process: 2 levels (20 units per process run).  Bake position: 2 levels (2 units per level per bake run).  Bake run: total of 10 levels (4 units per bake run; constraint - all positions must be filled, i.e. can't have 3 front and 1 back).  Assembly process: 2 levels (20 units per level; constraint - due to schedule, the first 5 bake runs have to go into the first build, second 5 in the second build).

My initial plan was to do a split-split plot design with bake run (only 5 levels) as main plot and oven position as subplot, while randomizing surface process into the subplots.  I would then effectively replicate the design in order to block on assembly process (since I can't randomize into that due to time constraints).  The model would just test for main effects for now.  However, whenever I generate the design, I JMP would inevitably give me blocks that would want all four wafers to occupy the front or back position of the oven (or 3 and 1), which can't happen.  I've tried several different ways of setting my factors up and can't seem to find a solution for this constraint.

Two questions...  What is the best way of working with a constraint like this?  Is my initial plan to best way to approach this experiment?  Thank you in advance for your help.

statman · Answer

It is difficult to provide advice about a situation that I may not completely understand.  I have some questions/comments first:

1. Why are you including surface process in the screening experiment if you already know it has a significant effect?  Why aren't you optimizing it?

2. You have evidence of front-back oven effect already, why don't you work to reduce the within oven variation?  Or are you trying to be robust to within oven variation?  Have you run any CoV sampling plans to understand the within and between oven variation?

3. You want to keep oven location in the experiment, you have 4 positions and you only allocate 2 levels?

4. Not sure why you have bake runs in the experiment?  It would seem that bake run is not an experimental factor.  For example, you wouldn't analyze the experiment and conclude bake run 5 is best so set there???  Why is there run-to-run variation?

5. You can potentially handle the bake run-to-run variation with blocking since the run-to-run variation is noise?

I would use directed sampling to understand why there is run-to-run variation.

6. Perhaps a strip-block would be better to handle the multiple positions within bake run? See Box and Jones "Split-plot designs for robust product experimentation".

7. Yes, a split-plot may be appropriate for handling the restriction on process levels.

8. You would not want to confound the process factor with the block.  Blocking is strategy to handle noise.  It allows you to increase the precision of detecting factor effect while increasing inference space.

Dan_Obermiller · Answer

On processes that are complicated, there is always a good chance that I am missing something. But I wonder if you really only need a split-plot design.

Bake Run is a hard-to-change factor with 5 levels (not sure how this number of levels came about, but just going with what you said).

All of the following are "easy-to-change":

Surface prep is a 2-level factor.

Oven position is a 4-level factor.

Assembly process is a 2-level factor.

During design creation, specify 4 runs per whole plot.

Here is the script for the design. Am I missing anything?

DOE(
	Custom Design,
	{Add Response( Maximize, "Y", ., ., . ),
	Add Factor( Categorical, {"L1", "L2"}, "Surface Process", 0 ),
	Add Factor( Categorical, {"L1", "L2", "L3", "L4"}, "Bake Position", 0 ),
	Add Factor( Categorical, {"L1", "L2"}, "Assembly Process", 0 ),
	Add Factor( Categorical, {"L1", "L2", "L3", "L4", "L5"}, "Bake Run", 1 ),
	Set Random Seed( 126371371 ), Number of Starts( 813 ), Add Term( {1, 0} ),
	Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {3, 1} ), Add Term( {4, 1} ),
	Add Alias Term( {1, 1}, {2, 1} ), Add Alias Term( {1, 1}, {3, 1} ),
	Add Alias Term( {1, 1}, {4, 1} ), Add Alias Term( {2, 1}, {3, 1} ),
	Add Alias Term( {2, 1}, {4, 1} ), Add Alias Term( {3, 1}, {4, 1} ),
	Set N Whole Plots( 10 ), Set Sample Size( 40 ), Simulate Responses( 0 ),
	Save X Matrix( 0 ), Make Design, Set Run Order( Keep the Same ), Make Table}
)