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Definition of “Resolution” The length of the shortest word in the defining relation is called the resolution of the design. Resolution describes the degree to which estimated main effects are aliased (or confounded) with estimated 2-level interactions, 3-level interactions, etc.
DOE Glossary. Alias. Two or more effects are said to be aliased in an experiment if these effects cannot be distinguished from each other. This happens when the columns of the design matrix corresponding to these effects are identical.
Aliasing, also known as confounding, occurs in fractional factorial designs because the design does not include all the combinations of factor levels. The alias structure describes the confounding pattern that occurs in a design. Terms that are confounded are also said to be aliased.
Resolution: A term which describes the degree to which estimated main effects are aliased (or confounded) with estimated 2-level interactions, 3-level interactions, etc. In general, the resolution of a design is one more than the smallest order interaction that some main effect is confounded (aliased) with.
Confounding. If the number of factors or levels increase in a factorial experiment, then the number of treatment combinations increases rapidly. When the number of treatment combinations is large, then it may be difficult to get the blocks of sufficiently large size to accommodate all the treatment combinations.
Use of fractional factorial designs. The basic purpose of a fractional factorial design is to economically investigate cause-and-effect relationships of significance in a given experimental setting. This does not differ in essence from the purpose of any experimental design.
Factorial design involves having more than one independent variable, or factor, in a study. Factorial designs allow researchers to look at how multiple factors affect a dependent variable, both independently and together. Factorial design studies are named for the number of levels of the factors.
Factorial designs are more efficient than FAT experiments. They provide more information at similar or lower cost. They can find optimal conditions faster than FAT experiments. Factorial designs allow additional factors to be examined at no additional cost.

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