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.