Consider the constrained mixture problem in Exercise 12.12. (a) Find a 15-point design for this…

Consider the constrained mixture problem in Exercise 12.12.

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(a) Find a 15-point design for this experiment using the
distance criterion, assuming that you are not required to replicate any points.

(b) Find an 18-point design for this experiment using the
distance criterion.

Assume that four runs must be replicates.

(c) Construct an FDS plot for the designs in parts (a) and
(b).

(d) Which design would you recommend?

Exercise 12.12

A four-component mixture experiment is subject to the
following constraints on the component proportions:

(a) Suppose that the experimenter wishes to fit a quadratic
model to the response. Identify a set of candidate points that the experimenter
should consider in the selected design.

(b) Find a D-optimal design for this experiment with n = 15
runs, assuming that you are not required to replicate any points.

(c) Find a D-optimal design for this experiment with n = 18
runs, assuming that four of these runs must be replicates.

(d) Find I-optimal designs for this experiment with n = 15
and n = 18 runs.

(e) Construct an FDS plot for the four designs in parts (b),
(c), and (d).

(f) Which design would you recommend?