Design of Experiments (DOE)
In this context, the term experiment refers to a situation where one is interested in the effect of one or more factors on a response. For example, one might be interested in the effect of cutting speed, cutting angle, and tool geometry, on the quality of a product. More generally speaking, design of experiments is a subject area that addresses how best to statistically design experiments in industry, and how best to analyze data that result from such experiments.
Using experimental designs, one can obtain a large amount of information about the effects of several factors on a response with a relatively small number of experimental runs. For example, one can test the effects of five factors on a response using only eight experimental trials. Experimental designs are efficient ways of experimenting with several factors.
In many processes, the experimental factors interact, that is, their relationship to the response of interest depends upon the mutual settings of the factors – one cannot individually characterize the effect of a single factor on the response because the nature of the effect will change if other experimental factor settings change. Statistically designed experimentation is the only way to find and characterize interactions among multiple experimental factors.
To choose an appropriate experimental design, one must understand the factors of interest, and how they can be manipulated in the course of running an experiment. One must also choose a design that is appropriate for the goal of the experiment. For example one might simply be interested in determining which factors affect the response, or one might want to optimize a response as a function of a set of factors. Depending on the specific situation at hand, one might use blocking, a fractional factorial design, a split plot design, a response surface design (central composite design or BoxBehnken design), or a mixture design.
Robust parameter design makes extensive use of design of experiments. Here, one is interested in minimizing variation as well as bringing a process to target. Shat models and direct variance modeling are based on experimental designs and require optimization of both the mean and the variance.

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