Statistica Sinica 21 (2011), 1541-1555
doi:10.5705/ss.2008.314

SOME THEORY FOR CONSTRUCTING GENERAL

MINIMUM LOWER ORDER CONFOUNDING DESIGNS

Jie Chen and Min-Qian Liu

Nankai University

Abstract: General minimum lower order confounding (GMC) is a newly proposed design criterion that aims at keeping the lower order effects unaliased with one another to the extent possible. This paper shows that for $5N/16<n\leq N/2$, $9N/32< n\leq5N/16$, and $17N/64< n\leq9N/32$, all GMC designs with $N$ runs and $n$ two-level factors are projections of maximal designs with $N/2$, $5N/16$, and $9N/32$ factors, respectively. Furthermore, it provides immediate approaches to constructing these GMC designs from the respective maximal designs; these approaches can produce many more GMC designs than the existing computer search method.

Key words and phrases: Alias set, general minimum lower order confounding, maximal design, minimum aberration.