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Next Page: Integration with Block Execution
A variety of experimental designs are incorporated into
DOE/Opt [19]. A nominal design generates a
single run with nominal (default) values for all selected block
inputs. A center point design is similar, but uses the midpoint
value (between the maximum and minimum limits) for all selected
inputs. Note that the range for input values may be specified
directly, as deltas from the default value (e.g. ``+5''), or
as percentages from the default value (e.g. ``-10%''). The
axial design includes center points, and points at the minimum
and maximum of each input while holding other inputs to their nominal
values. The Box Wilson design includes the center point, and
axial points and corner points distributed around an n-dimensional
sphere circumscribing the cuboid defined by the input minima and
maxima [20]. We have found two variants of the
conventional Box-Wilson design to be useful. The
Box-Wilson (inscribed) modifies the design by distributing axial and
corner points on an n-dimensional sphere inscribed within the
cuboid [21]. This has the benefit that no experimental points
will be outside the input ranges, but results in models that are not
well defined in the corners of cuboid. The Box-Wilson on a cube
stretches the corner points to lie on the cuboid corners to achieve
more complete coverage of the input parameter space. The
full-factorial design produces a uniform grid with user-specified
density covering the input parameter space. Other conventional
designs, including Box-Behnken and half fractional, (as
well as the half fraction complement for augmenting a screening
design), are provided [19]. Finally, Latin
hypercube sampling (LHS) [22] provides an orthogonal
array that randomly samples the entire design space broken down into
equal-probability regions (where
is the number of runs, and
is the number of input variables). LHS can be looked upon as a
stratified Monte Carlo sampling where the pairwise correlations can be
minimized to a small value (which is essential for uncorrelated
parameter estimates) or else set to a desired value [23].
LHS is especially useful in exploring the interior of the parameter
space, and for limiting the experiment to a fixed (user specified)
number of runs. All designs are generated algorithmically, with the
exception of Box-Behnken designs which use table lookups. Latin
hypercube samples are generated via an interface to LHS software from
Sandia National Laboratories [24].