A nickel-titanium alloy is used to make components for jet turbine aircraft engines. Cracking is a potentially serious problem in the final part because it can lead to non-recoverable failure. A test is run at the parts producer to determine the effects of four factors on cracks. The four factors are pouring temperature (A), titanium content (B), heat treatment method (C), and amount of grain refiner used (D). Two replicates of a 24 design are run, and the length of crack (in mm ×10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown below.

(a) Estimate the factor effects. Which factor effects appear to be large?
(b) Conduct an analysis of variance. Do any of the factors affect cracking? Use a = 0.05.
(e) Is there an indication that any of the factors affect the variability in cracking?
(d) The residuals show a violation of the assumptions. It appears that the data would be
better fit using two separate models.
(e) It does not appear than any of the variables affect the variability in cracking.
(f) What recommendations would you make regarding process operations? Use interaction and/or main effect plots to assist in drawing conclusions.
(c) yˆ 11.988 1.509A 1.988B 1.798C  0.979D  0.967AB  2.004AC

TABLE 13E.6 Crack Experiment for Exercise 13.19 Replicate Treatment ABD Combination 7.0376376 14.707 15.219 1635 12089 17273 17815 10.403 10.151 4.368 4.098 9.3609.253 13.440 12923 8.561 8.951 16.867 17.052 13.876 13.658 19.824 19.639 1846 12337 6.125 5904 11.190 10935 15.653 15.053 ab Ge be ad bd cd aod bed abed