Zhang et al. (Stat Sinica 18:1689–1705, <CitationRef CitationID="CR15">2008</CitationRef>) introduced an aliased effect-number pattern for two-level regular designs and proposed a general minimum lower-order confounding (GMC) criterion for choosing optimal designs. All the GMC <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$2^{n-m}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msup> <mn>2</mn> <mrow> <mi>n</mi> <mo>-</mo> <mi>m</mi> </mrow> </msup> </math> </EquationSource> </InlineEquation> designs with <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$N/4+1\le n\le...</equationsource></inlineequation></equationsource></equationsource></inlineequation></citationref>

Motivated by the effect hierarchy principle, Zhang et al. (Stat Sinica 18:1689–1705, <CitationRef CitationID="CR17">2008</CitationRef>) introduced an aliased effect number pattern (AENP) for regular fractional factorial designs and based on the new pattern proposed a general minimum lower-order confounding (GMC) criterion for choosing...</citationref>

Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considering the blocking factor. In this paper, the...