OFAT = One Factor at A Time
Supporting References
DOE = Design of Experiments, aka Statistically Designed Experiment
OFAT requires more effort and data, while providing less information than DOE.
OFAT is not 'orthogonal' and usually does not allow the estimation of interactions between factors.
OFAT extrapolates within the design space, while DOE interpolates.
Using three or more levels in OFAT commonly leads some to believe that they can estimate higher-order effects (quadratic, cubic, etc.), but this is not an effective method. See Three Level Factorial Design Matrix for an improved approach. Also note Central Composite designs (CCD).
OFAT does not provide an effective way to add to the Design Structure in subsequent designs.
OFAT tends to ignore the many pitfalls of not using a randomized order to testing the various treatments.