Suppose that you need to design an experiment to fit a quadratic model over the region 1 x i 1, i 1, 2 subject to the constraint x 1 x 2 1 If the constraint is violated, the process will not work properly You can afford to make no more than n 12 rum Set up the following designs (a) An inscribed CCD...

a An inscribed CCD with center point at x1 x2 0 would have a design where the center point is at the ...

Suppose that you need to design an experiment to fit a quadratic model over the region -1

Question:

Suppose that you need to design an experiment to fit a quadratic model over the region -1 ≤ x_i≤ +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 rum 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.

(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 part (c).

(g) Which design would you prefer? Why?

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