In the grill defects experiment described in Problem 8-29, a variation of the square root transformation was employed in the analysis of the data. Use the Box-Cox method to determine if this is the appropriate transformation.

Problem 8-29

A 16-run fractional factorial experiment in nine factors was conducted by Chrysler Motors Engineering and described in the article "Sheet Molded Compound Process Improvement," by P. I. Hsieh and D. E. Goodwin (Fourth Symposium on Taguchi Methods, American Supplier Institute, Dearborn, MI, 1986, pp. 13-21). The purpose was to reduce the number of defects in the finish of sheet-molded grill opening panels. The design, and the resulting number of defects, c, observed on each run, is shown below. This is a resolution III fraction with generators E = BD, F = BCD, G = AC, H = ACD, and J = AB.

 

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А В С D E F G H J Ve F&T's Modification Run 1 56 7.48 7.52 2 17 4.12 4.18 3 2 1.41 1.57 4 4 2.00 2.12 3 1.73 1.87 4 2.00 2.12 7 50 7.07 7.12 8 2 1.41 1.57 1 1.00 1.21 10 0.00 0.50 11 3 1.73 1.87 12 12 3.46 3.54 13 3 1.73 1.87 14 4 2.00 2.12 15 0.00 0.50 16 0.00 0.50 + + 1 | + + + I| + + + I | + + + + + + + + | + + + + + + + + | +1 + | + +