A General Minimum Lower-Order Confounding Criterion for Two-Level Regular Designs

摘要

Based on the hierarchical ordering principle of factorial effects in experimental design, we propose an aliased effect-number pattern (AENP) as a criterion to judge a two-level regular design; such a pattern contains the basic information of non-aliased effects as well as effects aliased at varying degrees in a design. A design that sequentially maximizes the numbers in the AENP is called a general minimum lower-order confounding (GMLOC) design. The new criterion is thus called a GMLOC criterion and several results follow. First, the word-length pattern, as the core of the minimum aberration (MA) criterion, is a function of the AENP, thus the MA criterion can be considered as a special case of the new criterion. The same also holds for the clear effects criterion under the hierarchical ordering principle. Furthermore,since the estimation capacity of a design can be calculated as a function of the new pattern, its corresponding criterion can be treated as a special case of the GMLOC criterion as well. From the new pattern, certain ties between the MA and clear effects criteria are revealed. In addition, we introduce in this paper a concept of estimation ability for regular designs, and infer that a GMLOC design is simply a design with the best estimation ability. At last, a simple algorithm for computing the AENP is provided. All the GMLOC designs for 16 and 32 runs and some comparisons with MA designs are tabulated in the Appendix.