Suppose that in Problem 6-15, only a one-half fraction of the 2⁴ design could be run. Construct the design and perform the analysis, using the data from replicate I.

Problem 6-15. 

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 nonrecoverable failure. A test is run at the parts producer to determine the effect 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 x 10-2) induced in a sample coupon subjected to a standard test is measured. The data are shown in the following table:

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Replicate Treatment Combination A B C D I II (1) 7.037 6.376 14.707 15.219 11.635 12.089 ab 17.273 17.815 10.403 10.151 ас 4.368 4.098 + bc 9.360 9.253 abc 13.440 12.923 d 8.561 8.951 ad 16.867 17.052 bd 13.876 13.658 abd 19.824 19.639 cd 11.846 12.337 аcd 6.125 5.904 bcd 11.190 10.935 abcd 15.653 15.053 + + + + + + + + + + + + 1 +II + + + I +I +I +