Theory of J-characteristics for fractional factorial designs and projection justification of minimum G2-aberration

Deng & Tang (1999) introduced the generalised resolution and minimum G-aberration criteria for assessing nonregular fractional factorials. In Tang & Deng (1999), a relaxed variant of minimum G-aberration, called minimum G(2)-aberration, is proposed and studied. These criteria are defined using a set of J values, called J-characteristics. In this paper, we show that a factorial design is uniquely determined by its J-characteristics just as a regular factorial design is uniquely determined by its defining relation. The theorem is given through an explicit formula that relates the set of design points to that of J-characteristics. Through this formula, projection justification of minimum G(2)-aberration is established.