A General Minimum Lower-Order Confounding Criterion for Two-Level Regular Designs
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.
Clear effects criterion Estimation ability Estimation capacity Hierarchical ordering principle Minimum aberration Minimum lower-order confounding,Regular design.
Runchu Zhang Shengli Zhao Peng Li Mingyao Ai
LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, China LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, China;School of Mathema LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
国际会议
2006 International Conference on Design of Experiments and Its Applications(2006实验设计及其应用国际会议)
天津
英文
2006-07-09（万方平台首次上网日期，不代表论文的发表时间）