5.
Process Improvement
5.5.
Advanced topics
5.5.2.

What is a computeraided design?


Computeraided designs are generated by a computer algorithm and
constructed to be optimal for certain models according to one of many
types of optimality criteria

Designs generated from a computer algorithm are referred to as
computeraided designs. Computeraided designs are experimental designs
that are generated based on a particular optimality criterion and are
generally 'optimal' only for a specified model. As a result, they are
sometimes referred to as optimal designs and generally do not satisfy
the desirable properties such as independence among the estimators that
standard classical designs do. The design treatment runs that are
generated by the algorithms are chosen from an overall candidate
set of possible treatment combinations. The candidate set consists of
all the possible treatment combinations that one wishes to consider in
an experiment.

Optimality critieria

There are various forms of optimality criteria that are used to
select the points for a design.

DOptimality

One popular criterion is
Doptimality, which seeks to maximize X'X, the determinant
of the information matrix X'X of the design. This criterion
results in minimizing the generalized variance of the parameter
estimates based on a prespecified model.

AOptimality

Another criterion is Aoptimality, which seeks to minimize the
trace of the inverse of the information matrix. This criterion results
in minimizing the average variance of the parameter estimates based on
a prespecified model.

GOptimality

A third criterion is Goptimality, which seeks to minimize the
maximum prediction variance, i.e., minimize
max. [d=x'(X'X)^{1}x], over a specified set of design points.

VOptimality

A fourth criterion is Voptimality, which seeks to minimize the
average prediction variance over a specified set of design points.

Optimality of a given design is model dependent

Since the optimality criterion of most computeraided designs is based
on some function of the information matrix, the 'optimality' of a given
design is model dependent. That is, the experimenter must specify a
model for the design and the final number of design points desired
before the 'optimal' design' can be generated. The design generated
by the computer algorithm is 'optimal' only for that model.
