11.14. A central composite design is run in a chemical vapor deposition process, resulting in the experimental data shown in Table P11.7. Four experimental units were processed simultaneously on each run of the design, and the responses are the mean and the variance of thickness, computed across the four units.

(a) Fit a model to the mean response. Analyze the residuals.

(b) Fit a model to the variance response. Analyze the residuals.

(c) Fit a model to ln(s2). Is this model superior to the one you found in part (b)?

(d) Suppose you want the mean thickness to be in the interval 450 ) 25. Find a set of operating conditions that achieves this objective and simultaneously minimizes the variance.

(e) Discuss the variance minimization aspects of part (d).
Have you minimized the total process variance?

Transcribed Image Text:

x1 x2 y -1 -1 360.6 6.689 1 -1 445.2 14.230 1 412.1 7.088 1 1 601.7 8.586 1.414 0 518.0 13.130 -1.414 0 411.4 6.644 0 1.414 497.6 7.649 0 -1.414 397.6 11.740 0 0 530.6 7.836 0 0 495.4 9.306 0 0 510.2 7.956 0 0 487.3 9.127