An experiment has been run in a process that applies a coating material to a wafer. Each run in the experiment produced a wafer, and the coating thickness was measured several times at different locations on the wafer. Then the mean y₁ and standard deviation y₂ of the thickness measurement was obtained. The data [adapted from Box and Draper (1987)] are shown in the table below: 

(a) What type of design did the experimenters use? Is this a good choice of design for fitting a quadratic model?

(b) Build models of both responses.

(c) Find a set of optimum conditions that result in the mean as large as possible with the standard deviation less than 60.

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Mean Std. Dev. Run Speed Pressure Distance y2 1 -1.000 -1.000 -1.000 24.0 12.5 0.000 -1.000 -1.000 120.3 8.4 3 1.000 -1.000 -1.000 213.7 42.8 4 -1.000 0.000 -1.000 86.0 3.5 5 0.000 0.000 -1.000 136.6 80.4 1.000 0.000 -1.000 340.7 16.2 7 -1.000 1.000 -1.000 112.3 27.6 8 0.000 1.000 -1.000 256.3 4.6 1.000 1.000 -1.000 271.7 23.6 10 -1.000 -1.000 0.000 81.0 0.0 11 0.000 -1.000 0.000 101.7 17.7 12 1.000 -1.000 0.000 357.0 32.9 13 -1.000 0.000 0.000 171.3 15.0 14 0.000 0.000 0.000 372.0 0.0 15 1.000 0.000 0.000 501.7 92.5 16 -1.000 1.000 0.000 264.0 63.5 17 0.000 1.000 0.000 427.0 88.6 18 1.000 1.000 0.000 730.7 21.1 19 -1.000 -1.000 1.000 220.7 133.8 20 0.000 -1.000 1.000 239.7 23.5 21 1.000 -1.000 1.000 422.0 18.5 22 -1.000 0.000 1.000 199.0 29.4 23 0.000 0.000 1.000 485.3 44.7 24 1.000 0.000 1.000 673.7 158.2 25 --1.000 1.000 1.000 176.7 55.5 26 0.000 1.000 1.000 501.0 138.9 27 1.000 1.000 1.000 1010.0 142.4