An article 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
below:
A B C D E Free Height, y
- - - - - 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
- - + + + 7.32, 7.44, 7.44
+ - + - + 7.56, 7.69, 7.62
- + + - + 7.18, 7.18, 7.25
+ + + + + 7.81, 7.50, 7.59
(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 free height for each run. Is there any
indication that any of these factors affects variability in 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 factorial design for five factors in 16 runs with higher resolution than this one?