A metal alloy is used to make components for aircraft engines. Cracking is a potentially serious problem in the final part, as it can lead to a non-recoverable failure. The objective of the experiment was to identify the key factors and possibly their interactions which have effects on cracks. Four factors were considered: pouring temperature (A), titanium content (B), heat temperature method (C), and the amount of grain refiner used (D). A full factorial experiment was conducted and the response of interest was the length of crack (in mm×10-2). Each trial condition was replicated twice. The data are given in the Table below. Calculate the factorial effects, including main effects, two-way, three-way and four-way interaction effects. Which factorial effects are significant for the crack length? Run A B C D Crack length
1 -1 -1 -1 1 6.48 5.87
2 -1 -1 -1 -1 13.53 14.00
3 -1 -1 1 1 10.71 11.12
4 -1 -1 1 -1 15.89 16.39
5 -1 1 -1 1 9.57 9.34
6 -1 1 -1 -1 4.02 3.77
7 -1 1 1 1 8.61 8.52
8 -1 1 1 -1 12.37 11.89
9 1 -1 -1 1 7.88 8.24
10 1 -1 -1 -1 15.52 15.69
11 1 -1 1 1 12.77 12.57
12 1 -1 1 -1 18.24 18.07
13 1 1 -1 1 10.90 11.35
14 1 1 -1 -1 5.64 5.43
15 1 1 1 1 10.30 10.06
16 1 1 1 -1 14.40 13.85