Taguchi Design

[#1]

Does anyone know how to design an experiment using Taguchi approach with following factors? 

Inner array:

X1 at 2 levels 

x2 at 2 levels

X3 at 4 levels 

Outer array: 

X4 at 2 levels

X5 at 2 levels  

JMP DoE option only handles factors at 3 levels, how do I get round it? is there a solution or a trick? 

Many thanks in advance 

[#2 · Accepted solution]

Just curious why you would want to do this?  I mean, Cross product arrays are a fantastic idea for robust design, but a 4-level factor? Is the 4-level factor continuous or categorical? While I know there are a number of 2-level orthogonal arrays, Taguchi, philosophically, suggests 3-level designs for the design factors (he doesn't really believe relationships are linear).  Also for the outer array, since you will have to have 4 combinations (3 DFs) you might as well add a third noise variable for the 3rd DF since you don't care about noise-by-noise interactions.

To the best of my recollection (this was a long time ago), the way Taguchi did it was to take three columns from the orthogonal array (3 DFs, same for a 4-level factor). That will give you 8 possible combinations.  Set those to 4 levels like this:

A	B	C		D
-1	-1	-1		1
1	-1	-1		2
-1	1	-1		3
1	1	-1		4
-1	-1	1		1
1	-1	1		2
-1	1	1		3
1	1	1		4

Don't use the 3 columns used to create the 4 level factor (obviously). But I could be completely wrong...LOL

[#3]

Thank you very much for your reply and sorry for the delay responding.  Your suggestion is simple and smart thank you! (why didn't I think of it myself ).

To answer your question, the four 4 levels are categorical. why? does it make a difference in design? 

[#4]

For industrial experiments, the primary reason for experimenting on factors at more than 2 levels is to add non-linear terms to the polynomial.  These terms are non-sensical for categorical factors. Since the factor is categorical, are you trying to "pick a winner" or understand causal relationships?  No need for more than 2 categories when trying to do the latter.

[#5]

Sorry for late reply, just saw your message. I am trying to "pick a winner ". . We have a good understanding for the effect of each process factor, what we don't know is which combination gives more robust results given all the other noise factors. does this make sense? 

[#6]

Philosophically, DOE is an effective (and often efficient) means of understanding causal structure.  If you are trying to pick a winner, you don't need DOE.  However, what you are trying to accomplish suggests you don't understand the causal structure (just design factor effects?).  IMHO, understanding causality requires you understand the relationships not only between design factors (this is a subset based on your hypotheses of significant factors), but with ALL potential significant factors including those that you are not willing to manage (noise).  In order to do this efficiently, you will need to vary the noise during your experimentation.  There are many strategies to do this including repeats, replicates, blocks and split-plots.  In most of these strategies it is inefficient to do more than 2 levels for the design factors as you begin to understand their robustness to noise.