One-factor-at-a-time method
Encyclopedia
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). Designed experiments remain nearly always preferred to OFAT with many types and methods available, in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above. 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), gives generally greater precision in effect estimation
.
Design of experiments
In general usage, design of experiments or experimental design is the design of any information-gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms are usually used for controlled 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
Ronald Fisher
Sir Ronald Aylmer Fisher FRS was an English statistician, evolutionary biologist, eugenicist and geneticist. Among other things, Fisher is well known for his contributions to statistics by creating Fisher's exact test and Fisher's equation...
, 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). Designed experiments remain nearly always preferred to OFAT with many types and methods available, in addition to fractional factorials which, though usually requiring more runs than OFAT, do address the three concerns above. One modern design over which OFAT has no advantage in number of runs is the Plackett-Burman
Plackett-Burman design
Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply....
which, by having all factors vary simultaneously (an important quality in experimental designs), gives generally greater precision in effect estimation
Efficiency (statistics)
In statistics, an efficient estimator is an estimator that estimates the quantity of interest in some “best possible” manner. The notion of “best possible” relies upon the choice of a particular loss function — the function which quantifies the relative degree of undesirability of estimation errors...
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