8.10. An article by J. J. Pignatiello Jr. and J. S. Ramberg in the Journal of Quality Technology (Vol. 17, 1985, pp.

198–206) describes 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 Table P8.1

(a) Write out the alias structure for this design. What is the resolution of this design?

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

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

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

(e) Is this the best possible design for five factors in 16 runs?
Specifically, can you find a fractional design for five factors in 16 runs with a higher resolution than this one?

Transcribed Image Text:

ABCDE Free Height 7.78 7.78 7.81 8.15 8.18 7.88 7.50 7.56 7.50 + 7.59 7.56 7.75 7.54 8.00 7.88 7.69 8.09 8.06 + 7.56 7.52 7.44 + + + + 7.56 7.81 7.69 7.50 7.25 7.12 7.88 7.88. 7.44 + ++ 7.50 7.56 7.50 7.63 7.75 7.56 + + + +++ +11+ 7.32 7.44 7.44 +++ 7.56 7.69 7.62 7.18 7.18 7.25 7.81 7.50 7.59