Minimum-Aberration
Two-Level Fractional Factorial Split-Plot Designs
Derek
Bingham and Randy R. Sitter
Technometrics, February
1999, Vol. 41, No. 1, pp. 62-70.
If the experimental runs of a
fractional factorial design cannot be completely randomized, then a split-plot
design is an option. The split-plot
(SP) treatment combinations are randomized within the whole plot (WP) units.
Minimum aberration (MA)
criteria differentiate among designs with the same resolution by the frequency
of short words. Note that there are situations where MA fractional factorial
split plot (FFSP) designs may not be desirable, such as the need for specific,
clear two-factor interactions.
WP factors are used in the SP
generators. The WP fractional
generators must be free of SP factors, and no word in the defining relation can
contain only one SP factor. Otherwise, the split-plot nature of the design is
destroyed. Addelman (1964) presented
some split-plot designs generated on this basis. Huang, Chen, and Voelkel
(1998) constructed a more extensive table by modifications of 2k-p
factorial designs.
These authors introduce an
algorithm for fractional factorial design (FFSP) that combines sequential
construction (Chen, Sun, and Wu, 1993) with a search table (Franklin and
Bailey, 1977). This algorithm is
described as more efficient than either of the two methods alone.
FFSP designs are presented in
two tables, in run sizes of eight and 16. The 16-run designs are MA. Several
examples and explanations, using a Yates order matrix and factor search table,
describe the mechanism of designing a FFSP.
The number of nonisomorphic designs for 16 runs in this report is larger
than the number reported by Huang, Chen, and Voelkel, and is due, presumably,
to the algorithm's ability to find treatment structures that do not have a
corresponding MA fractional factorial.
Methods of testing for
isomorphic design and other applications of the combined approach are also
described.
References:
Addelman, S. (1964), Technometrics, Vol. 6, No. 1, pp. 253-258.
Chen,J., Sun, D.X., and Wu,
C. F. J. (1993), International
Statistical Review, Vol. 61, No. 1, pp. 131-145.
Franklin, M. F., and Bailey,
R. A. (1977), Applied Statistics,
Vol. 40, pp. 321-326.
Huang, P., Chen, D, and
Voelkel, J. (1998), Technometrics, Vol.
40, No. 4, pp314-326.
Sharon Sheliga
October 30, 2000