DoE and ANOVA - 4 factor and 3 levels Taguchi design with 2 replicates

[Statistical Steven]

In Reply to Parent Post by Allattar

Correction.
Taguchi is not the best approach for analysing interactions.
ANOVA is the right approach to the analysis.

You would be better off with a standard factorial design here, with 2 levels per factor I think. Unless you have a specific reason why you need 3 levels per factor.
If you are fitting only linearity and you have numeric inputs you do not need 3 levels on each factor. You can use a centre points instead to check for curvature.

Just to add to your excellent response, if you have a four factor, two level study, the full factorial would be 16 runs. A 1/2 fraction would 8 runs. So you can run a single run at the center point.

[Miner]

In Reply to Parent Post by Statistical Steven

Miner -

I believe if you use a column of your Taguchi array for the interaction it would have to be the correct column where the interaction is confounded. Typically when this occurs you are not reducing the run total enough to justify its use. For example, assuming the OP was interested in only one ogf the interactions therefore reduced it to a three factor, 3 level design. This is just a 1/3 fractional factorial, so no need to use the Tachugi array per se.

Though, I agree it can be done, I have never seen it applied successfully.

You are correct about reserving the column where the confounding occurs. I did not claim that it was efficient, but in my earlier days when Taguchi was new, I have successfully used the approach many times. Now I have learned to do the same things in a more efficient manner.

For example, Box has shown how the inner and outer array approach can be done more efficiently using a Split-plot design. We learn new things. It does not make the old way wrong, just less efficient.

Before computers made the calculations easy, Taguchi's approach was great, because the math was easy. I date back to those days. I had to perform the calculations by hand for years before getting one of the first IBM PCs (pre-XT). That was his intent.

[Statistical Steven]

In Reply to Parent Post by Miner

You are correct about reserving the column where the confounding occurs. I did not claim that it was efficient, but in my earlier days when Taguchi was new, I have successfully used the approach many times. Now I have learned to do the same things in a more efficient manner.

For example, Box has shown how the inner and outer array approach can be done more efficiently using a Split-plot design. We learn new things. It does not make the old way wrong, just less efficient.

Before computers made the calculations easy, Taguchi's approach was great, because the math was easy. I date back to those days. I had to perform the calculations by hand for years before getting one of the first IBM PCs (pre-XT). That was his intent.

I still have the Taguchi workbooks with the different arrays and hand calculations. I am just surprised with software such as JMP and Minitab, we still have people trying to use methods that are not just inefficient, but sometimes the wrong application.

[Allattar]

I find Steven that it has to do with the Buzzword effect. Meeting lots of different people from different industries when someone mentions the word Taguchi I get a shiver down my spine.

These may be unfair generalisation so please correct me if you see otherwise.

If someone I meet says they have tried a Taguchi design they have used it becuase someone else told them that DOE is fantastic and to use taguchi.
There experience of DOE is only from what someone else told them and all they heard is Taguchi gave them good results.
They end up not using an outer array, they use a few levels on factors becuase they can, or becuase of checking for curvature.
Taguchi is used becuase they get lots of factors, with lots of levels with very few runs, again ignoring that they need an outer array, and ignoring the DF needed to find interactions.

Its also highly likely that they just pick a design and haven't checked on the diagrams to help place columns to find interactions if any are allowed.

Then I get asked why dont the results work very well.

I have met a few guys who knew what they where doing with Taguchi, and that always makes me feel better Problem is I find is as I mentioned above Taguchi is believed to be DOE.

I always try and urge anyone thinking about a Taguchi design to really really read up on them as in my opinion the hardest part of creating a Taguchi design is understanding how to place the factors, why you would use the different design types, and the importance of that outer array.

[Statistical Steven]

In Reply to Parent Post by Allattar

I find Steven that it has to do with the Buzzword effect. Meeting lots of different people from different industries when someone mentions the word Taguchi I get a shiver down my spine.

Taguchi is used becuase they get lots of factors, with lots of levels with very few runs, again ignoring that they need an outer array, and ignoring the DF needed to find interactions.

Have they tried a Plackett-Burman? The real appeal to Taguchi is the "over-saturation" of the model. I should not bash it, I just do not use it

[amandeep007]

In Reply to Parent Post by Statistical Steven

Just to add to your excellent response, if you have a four factor, two level study, the full factorial would be 16 runs. A 1/2 fraction would 8 runs. So you can run a single run at the center point.

sir i am using taguchi L9 array with 4 parametrs and 3 levels
can we working use 4 parametrs in L9 array on please suggest me sir i am very confused with it

[Miner]

In Reply to Parent Post by amandeep007

sir i am using taguchi L9 array with 4 parametrs and 3 levels
can we working use 4 parametrs in L9 array on please suggest me sir i am very confused with it

The L9 Taguchi orthogonal array will handle a maximum of 4 factors (parameters) at three levels each.

Be aware that the L9 is a resolution III design. This means that all of the main effects are confounded (aliased) with two-way interactions. This means that if you seem to have a significant factor, it may not actually be the factor, but may be its confounding interactions instead. The L9 is only suitable for use as a screening design. The results must ALWAYS be confirmed with a follow-up experiment.

If you are concerned with detecting curvature, you could run a 2^3 full factorial plus one center point for 9 experimental runs. This will not only detect any curvature, but will eliminate all confounding.