Overview

"Two roads diverged in a wood, and I I took the one less traveled by, And that has made all the difference."

-ROBERT FROST (FROM "THE ROAD NOT TAKEN")

The preceding chapters have all been opening acts for the main event design of experiments (DOE) geared for response surface methods (RSM). Assume that you are now approaching the optimum level for your response. Therefore, due to resulting curvature, two-level factorial designs will no longer provide sufficient information to adequately model the true surface. We must dig in at this stage and do more exploration via additional experimental runs at new levels in your factors.

Augmenting a Two-Level Factorial with Star Points to Fit Curvature

We now must deal with a fork in the road created by the discovery of significant curvature in response. The path usually taken in such cases requires running new factor combinations, typically drawn as stars, along the axes of the x space, resulting in a central composite design (CCD). It's important to keep in mind that this design is intended for sequential experimentation, not a one-shot approach, thus making it flexible for industrial process development. Figure 4-1 shows (for three factors) how the CCD is built up from:

1. Two-level factorial design (plus center points).

2. Axial points represented by stars (plus more center points).

Figure 4-1: Build-up of central composite design for three factors

The result, at the far right of Figure 4-1, is a composite design suited to response surface methods.

The stars in the design pictured...