5. Process Improvement
5.5. Advanced topics

5.5.2.

What is a computer-aided design?

Computer-aided 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 computer-aided designs. Computer-aided 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.

D-Optimality

One popular criterion is D-optimality, 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 pre-specified model.

A-Optimality

Another criterion is A-optimality, 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 pre-specified model.

G-Optimality

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

V-Optimality

A fourth criterion is V-optimality, 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 computer-aided 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.