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Factorial designs have been increasingly used in scientific investigations and technological development. The designs, through the use of matrices with all the treatment combinations, have been capable to effectively characterize the relationships between the variables of multi-factor experiments, assess the experimental variabilities, and derive mathematical functions that represent the behavior of the responses. Factorial designs were fractionalized, which substantially reduced the number of treatments without the loss of relevant information. The addition of central and star points to the factorial arrays has given them the orthogonality and rotatability characteristics, frequently used to fit models with curvature and identify critical regions of interest. Literature reports indicated that factorial designs, also called factorial experiments, were successfully applied in different types of investigations, including in cost evaluations and time-series studies. They were capable to estimate important features of the experiments, like the individual and combined effects of factors, the magnitude of residuals, additionally to express the relationships of the variables in polynomial equations, draw response surface and contour plots, and determine optimal combinations of parameters. In this review, the fundamental aspects of the Complete, Fractional, Central Composite Rotational and Asymmetrical factorial designs were conceptualized, and recent applications of these powerful tools were described.
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