Suppose that you need to design an experiment to fit a quadratic model over the region −1 ≤ xi ≤ +1, i = 1,2 subject to the constraint x1 + x2 ≤ 1. If the constraint is violated, the process will not work properly. You can afford to make no more than n = 12 runs. Set up the following designs:

(a) An “inscribed” CCD with center point at x1 = x2 = 0.

(b) An “inscribed” 32 factorial with center point at x1 =

x2 = −0.25.

(c) A D-optimal design.

(d) A modified D-optimal design that is identical to the one in part (c), but with all replicate runs at the design center.

(e) Evaluate the |(X′X)−1| criterion for each design.

(f) Evaluate the D-efficiency for each design relative to the D-optimal design in part (c).

(g) Which design would you prefer? Why?