An article in the Journal of Quality Technology (1985, Vol. 17, pp. 198€“206) described the use of a replicated fractional factorial to investigate the effect of five factors on the free height of leaf springs used in an automotive application. The factors are 

A = furnace temperature, 

B = heating time,

C = transfer time, 

D = hold down time, and 

E = quench oil temperature.

The data are shown in the following table.

(a) What is the generator for this fraction? Write out the alias structure.

(b) Analyze the data. What factors influence mean free height?

(c) Calculate the range of free height for each run. Is there any indication that any of these factors affect variability in free height?

(d) Analyze the residuals from this experiment and comment on your findings.

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Free Height 7.78 7.78 7.81 7,88 8.15 8.18 7.50 7.56 7.50 7.75 7.59 7.56 7.54 8.00 7.88 7.69 8.09 8.06 7.56 7.52 7.44 7.81 7.56 7.69 7.50 7.50 7.56 7,88 7.88 7.44 7.50 7.56 7.50 7.63 7.75 7.56 7.32 7.44 7.44 7.62 7.56 7.69 7.18 7.18 7.25 7,81 7.59 7.50 + + + |I + + + I + + I I + + I + I + I + I + I + I + I +I +