General minimum lower order confounding designs: An overview and a construction theory

For fractional factorial (FF) designs, Zhang et al. (2008) introduced a new pattern for assessing regular designs, called aliased effect-number pattern (AENP), and based on the AENP, proposed a general minimum lower order confounding (denoted by GMC for short) criterion for selecting design. In this paper, we first have an overview of the existing optimality criteria of FF designs, and then propose a construction theory for 2 n − m GMC designs with 33 N / 128 ≤ n ≤ 5 N / 16 , where N = 2 n − m is the run size and n is the number of factors, for all Nʹs and nʹs, via the doubling theory and SOS resolution IV designs. The doubling theory is extended with a new approach. By introducing a notion of rechanged (RC) Yates order for the regular saturated design, the construction result turns out to be quite transparent: every GMC 2 n − m design simply consists of the last n columns of the saturated design with a specific RC Yates order. This can be very conveniently applied in practice.