Consider the experiment in Exercise 14-19. Suppose that a center point with five replicates is added to the factorial runs and the responses are 45, 40, 41, 47, and 43.

(a) Estimate the experimental error using the center points. Compare this to the estimate obtained originally in Exercise 14-19 by pooling apparently non significant effects.

(b) Test for curvature with α = 0.05.

Exercise 14-19

An experiment was run in a semiconductor fabrication plant in an effort to increase yield. Five factors, each at two levels, were studied. The factors (and levels) were A = aperture setting (small, large), B = exposure time (20% below nominal, 20% above nominal), C = development time (30 and 45 seconds), D = mask dimension (small, large), and E = etch time (14.5 and 15.5 minutes). The following unreplicated 25 design was run:

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(1) = 12 = 35 = 52 = 15 = 22 45 = 65 9. a ae = 34 = 55 = 16 = 20 = 40 = 60 be abe ab ce ac ace bc abc bce abce = 6 de = 10 = 10 ad ade bde = 32 abd = 50 cd = 30 abde = 53 cde bd = 15 acde = 20 bcde = 41 abcde = 63 18 acd = 21 bcd = 44 abcd = 61