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.