An article in Solid State Technology (Vol. 29, 1984, pp. 281–284) describes the use of factorial experiments in photolithography, an important step in the process of manufacturing integrated circuits. The variables in this experiment

(all at two levels) are prebake temperature (A), prebake time (B), and exposure energy (C), and the response variable is delta-line width, the difference between the line on the mask and the printed line on the device. The data are as follows:

(1)  2.30, a  9.87, b  18.20, ab  30.20, c  23.80, ac  4.30, bc  3.80, and abc  14.70.

(a) Estimate the factor effects.

(b) Suppose that a center point is added to this design and four replicates are obtained: 10.50, 5.30, 11.60, and

7.30. Calculate an estimate of experimental error.

(c) Test the significance of main effects, interactions, and curvature.

At   0.05, what conclusions can you draw?

(d) What model would you recommend for predicting the delta-line width response, based on the results of this experiment?

(e) Analyze the residuals from this experiment, and comment on model adequacy.