The Box-Behnken design that requires only three levels to run an experiment. It is a special 3-level design because it does not contain any points at the vertices of the experiment region.
Screening designs are typically of resolution III. The reason is that resolution III designs permit one to explore the effects of many factors with an efficient number of runs. Sometimes designs of resolution IV are also used for screening designs. In these designs, main effects are confounded with, at worst, three-factor interactions.
And also we use 3 factor in Full Factorial Design .
Taguchi designs can have factors with several levels, although two and three level designs are the most common. The L18 design is perhaps the most popular.
So best choice for a 2-level, 2-factor design is Tanguchi L18 Design.
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