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 G2‐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 G2‐aberration is established.