A two-level factorial design can be uniquely represented by a polynomial indicator function. Therefore, properties of factorial designs can be studied through their indicator functions. This paper shows that the indicator function is an effective tool in studying two-level factorial designs. The indicator function is used to generalize the aberration criterion of a regular two-level fractional factorial design to all two-level factorial designs. An important identity of generalized aberration is proved. The connection between a uniformity measure and aberration is also extended to all two-level factorial designs.
"Indicator function and its application in two-level factorial designs." Ann. Statist. 31 (3) 984 - 994, June 2003. https://doi.org/10.1214/aos/1056562470