# One-factor-at-a-time method

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One-factor-at-a-time method

The one-factor-at-a-time method (or OFAT) is a method of designing experiments involving the testing of factors, or causes, one at a time instead of all simultaneously. Prominent text books and academic papers currently favor factorial experimental designs, a method pioneered by Sir Ronald A. Fisher, where multiple factors are changed at once. The reasons stated for favoring the use of factorial design over OFAT are:

1. OFAT requires more runs for the same precision in effect estimation
2. OFAT cannot estimate interactions
3. OFAT can miss optimal settings of factors

Despite these criticisms, some researchers have articulated a role for OFAT and showed they can be more effective than fractional factorials under certain conditions (number of runs is limited, primary goal is to attain improvements in the system, and experimental error is not large compared to factor effects, which must be additive and independent of each other).[1][2] Designed experiments remain nearly always preferred to OFAT with many types and methods available,[3] in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above.[4] One modern design over which OFAT has no advantage in number of runs is the Plackett-Burman which, by having all factors vary simultaneously (an important quality in experimental designs),[5] gives generally greater precision in effect estimation.

## References

1. ^ Friedman, M., and Savage, L. J. (1947), “Planning Experiments Seeking Maxima,” in Techniques of Statistical Analysis, eds. C. Eisenhart, M. W. Hastay, and W. A. Wallis, New York: McGraw-Hill, pp. 365-372.
2. ^ Daniel , C. (1973) ,“One-at-a-Time Plans,” Journal of the American Statistical Association 68, 353-360
3. ^ See Category: Experimental design, at bottom.
4. ^ Czitrom (1999) "One-Factor-at-a-Time Versus Designed Experiments", American Statistician, 53, 2.
5. ^ Ibid. Czitrom.

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