In the design of experiments, the Design Resolution is a key criteria for selecting a fractional factorial design:
Resolution III 
R_{III} 
two factor interactions are aliased with main effects 
Resolution IV 
R_{IV} 
two factor interactions are aliased with other two factor interactions, but not with main effects. Main effects are aliased with three factor interactions. 
Resolution 5 
R_{V} 
two factor interactions are not aliased with each other, but are aliased with three factor interaction 
An R_{III} design would usually be used for screening experiments. There would rarely be any point in going beyond an R_{V} design.
In general the resolution is the length of the shortest word in the defining relationship.
