# y hat models for 3-level factor DOE designs

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• #52524

howe
Participant

Ran into this issue the other day when an engineer was wanting to develop a transfer function (y hat model) to explain the relationship of three design factors (dimensions) on the output response (slide efforts) for his product.  The concern was that there was a good possibility of some nonlinear relationships, so we desided to run a full factor DOE (3 factors) with 3 levels.  Sure enough some nonlinear main effects plots were developed, but the thing that caught me off guard was no Coefficiants in the output (Minitab) to build my y hat equation.  Is this the case for any 3 or more level DOE when things act nonlinear?  In this case do i use the DOE results to determine what factors are importand and then build my math model by hand using nonlinear stepwise regression techniques?  I will run into this issue again with multi-level DOE’s and engineers wanting to use the y hat models for predictions.  thanks in advance

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#184827

Mikel
Member

Sounds like a software issue. You using something like DOE kiss?

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#184828

Paco
Participant

You should have an equation with coefficients, try a counfoundig design in Minitab, or try DX7 and you’ll get your eaqution

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#184837

howe
Participant

In a DOE design with factors having more then 2-levels does the Minitab software have a way to deal with the second order terms found in a nonlinear quadratic equation (i.e. calculating and determining their coefficiants for the y hat model)?

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#184840

Mikel
Member

Yes, Use the RSM option under DOE.

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#184841

Remi
Participant

hai mike,
if 3-level design (cube with middle of faces/ribs): analyse with Stat->DoE-> Response Surface Design. Analysing is comparible to when using Stat->DoE-> Factorial. only ABC and higher order terms will not be present and A^2 (written as A*A) etc will be. Analysis wil give coefficients for each of the terms in the quadratic model and p-values on the significance of the term if extra d.f. present. Removing of terms to simplify the model is also the same. The optimizer can find optimum inside the area investigated (top of curve). Residuals are analogous.
If at least one term> 3 levels: bad luck No higher order polynomial model can be calculated. Only values at investigated points will be shown and straight lines will connect the values. Analysis can be done via Stat->DoE-> Factorial but you have to choose General Design when defining the design.
‘Dirty’ Trick. Even when you have >3 levels you could analyse it as either quadratic (use RSM) or linear model (use Factorial). Just define the data as such a design. Difference is wether A*A or ABC will be analysed as terms (you could try them both to see which one you like best).When analysing it this way Mintab will ‘complain’ that the design is not balanced; botched runs etc; but the analysis will be ok.In fact you will force Mtab to fit the data to a quadratic or linear model. So if your data is in reality very different from such a model the model that you find will have no predictive value (=be of nu use).
Good luck,
Remi

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