5.
Process Improvement
5.4.
Analysis of DOE data
5.4.3.

How to model DOE data


DOE models should be consistent with the goal of the experiment

In general, the trial model that will be fit to DOE data should be
consistent with the goal of the experiment and has been
predetermined by the goal of the experiment and the experimental
design and data collection methodology.

Comparative designs

Models were given earlier for comparative designs
(completely randomized
designs, randomized
block designs and
Latin square designs).

Full factorial designs

For full factorial designs with k factors (2^{k}
runs, not counting any center points or replication runs), the full model
contains all the main effects and all orders of interaction terms.
Usually, higherorder (three or more factors) interaction terms are
included initially to construct the normal (or halfnormal) plot of
effects, but later dropped when a simpler, adequate model is fit.
Depending on the software available or the analyst's preferences,
various techniques such as normal or halfnormal plots, Youden plots,
pvalue comparisons and stepwise regression routines are used to
reduce the model to the minimum number of needed terms. An example
of model selection is shown later in this section and an example of Yates algorithm
is given as a case study.



Fractional factorial designs

For fractional factorial screening designs, it is necessary to know
the alias structure in order to write an appropriate starting model
containing only the interaction terms the experiment was designed
to estimate (assuming all terms confounded with these selected terms
are insignificant). This is illustrated by the fractional factorial
example later in this
section. The starting model is then possibly reduced by the same
techniques described above for full factorial models.

Response surface designs

Response surface initial models include quadratic terms and may
occasionally also include cubic terms. These models were described
in section 3.

Model validation

Of course, as in all cases of model fitting, residual
analysis and other tests of model fit are used to confirm or adjust
models, as needed.
