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Taguchi Design

MoNa1324

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

Accepted answers

statman

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

DOEpossibly.jmp

All comments

statman

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

DOEpossibly.jmp

MoNa1324

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?

statman

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.

MoNa1324

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?