Help with Minitab Taguchi aplication

[Durmus]

Hello, I have a question about using minitab DOE Taguchi design aplication. When I have a three factor theree level (L9) Taguchi design and apply Minitab for the analysis I have a problem to understand the results of analysis for the coefficients
Term Coef SE Coef T P
Constant 0.99915 0.008884 112.465 0.000
A 1 -0.04168 0.012564 -3.317 0.080
A 2 0.10980 0.012564 8.739 0.013
B 1 0.11209 0.012564 8.921 0.012
B 2 0.11209 0.012564 8.921 0.012
C 1 -0.14533 0.012564 -11.567 0.007
C 2 0.05945 0.012564 4.731 0.042
Here the results of coefficients are given as A1 and A2 also for B and C are the same. What is the meaning of A1 and A2 here?

 

[Miner]

Do you absolutely have to use the Taguchi approach? Or do you need to analyze an experiment that you ran using a Taguchi orthogonal array? If the latter, try analyzing the results using GLM instead.

If you must use the Taguchi approach, I would need to see your MPJ file to answer.

 

[Durmus]

Do you absolutely have to use the Taguchi approach? Or do you need to analyze an experiment that you ran using a Taguchi orthogonal array? If the latter, try analyzing the results using GLM instead.

If you must use the Taguchi approach, I would need to see your MPJ file to answer.

Thank you very much for the reply.
Yes I have to use Minitab for the Taguchi design because I am trying to understand the Taguchi with minitab. Here I have attached MPJ file for the problem. I appreciate your help to understand this output

 

[Miner]

Ugh. Taguchi had some great ideas (e.g., parameter design), but this particular analysis approach was not one of them.

Okay, you cannot interpret the column labeled Coef the same as the coefficient in a regression model, or even in an ANOVA. It is not a slope coefficient, but a delta from the Grand Mean.

For example, the Constant (1.12222) is the Grand Mean. The Coefficient for level A1 is -0.00556. The mean for level A1 = 1.12222 - 0.00556 = 1.11666 or as shown in your Response Table for Means rounded off to 1.117. The Mean for A2 = 1.12222 + 0.01444 = 1.13666 or 1.137. I do not know why A3 is ignored.

The same hold true for B & C. If you want to know what the mean for a combination of different levels, add their coefficients to the grand mean.

 

[GretaGarbo]

When I have a three factor theree level (L9) Taguchi design

That is just a usual Latin square design.

If I understand Miner correctly, it sounds like the software is using “the classical sum to zero parametrization”. There is nothing wrong with that one. It will give the same “results” (i.e. conclusions) as an anova with regression on dummy variables. The classic sum-to-zero-method will also create dummy variables:
A '1' for the first dummy variable when the factor is on level 1.
A '0' for the first dummy variable when the factor is on level 2.

A '0' for the second dummy variable when the factor is on level 1.
A '1' for the second dummy variable when the factor is on level 2.
But:
A '-1' for the first dummy variable when the factor is on level 3.
A '-1' for the second dummy variable when the factor is on level 3.

The dummy variables in the sum-to-zero will be coded as (1, 0 and -1). In the “corner point parametrization”= dummy variable parametrization it will be (1 and 0). So they are linear transformations of each other and least squares in linear regression is invariant to linear transformations so both will lead to the same conclusions.

The parameter A3 is omitted from the printout because of the “dummy variable trap”, that since it is not possible with a three level variable to both estimate the intercept (the constant) and three effect parameter. That would lead to linear dependence, thus “problems”. The A3 paramete can be calculated as -(A1+A2). The the mean at level 3 will be: intercept +A3 = intercept – (A1+A2).

But maybe it is easier to just run a standard anova (as Miner suggest).

I hope that the software does not print some of Taguchis strange ideas about signal-to-noice-ratios.

 

[Miner]

I hope that the software does not print some of Taguchis strange ideas about signal-to-noice-ratios.

Unfortunately, it does. Minitab faithfully reproduced the traditional Taguchi analysis exactly.

Taguchi's parameter design concept is excellent, but the use of S/N ratios is not. I prefer to analyze the means and the Ln(StdDev) separately. In his defense, he developed these approaches before the prevalence of personal computers, and knew that the only way they would gain acceptance was if they could easily be calculated by hand and be understood by engineers (who would already be familiar with the concept of S/N Ratios).

 

[Durmus]

Thank you very much for the explanation for the coefficients but as you said no value for A3 or B3 C3. Now have tried for level case then there is A3 but then no A4. So it goes all the way like this. But, isn't there a way of giving a model equation? Then how can we predict future observations?