A GENERAL MINIMUM LOWER-ORDER CONFOUNDING CRITERION FOR TWO-LEVEL REGULAR DESIGNS

作者：Zhang Runchu^*; Li Peng; Zhao Shengli; Ai Mingyao

来源：Statistica Sinica, 2008, 18(4): 1689-1705.

• Clear effects criterion
• effect hierarchy principle
• estimation ability
• estimation capacity
• minimum aberration

Based on the effect hierarchy principle in experimental design, an aliased effect-number pattern (AENP, or AP for short) is proposed to judge two-level regular designs; it contains the basic information of all effects aliased with other effects at varying severity degrees in a design. Based on the AENP, a general minimum lower-order confounding (GMLOC, or GMC for short) criterion is proposed, and several results follow. First, the word-length pattern, as the core of the minimum aberration (MA) criterion, is a function of the AENP. The same also holds for the clear effects (CE) criterion. Furthermore, the estimation capacity (EC) of a design can be also calculated as a function of the new pattern, and links between the MA and CE criteria are discovered. In addition, a concept of estimation ability is introduced, and it is concluded that a GMC design is the one with the best estimation ability. Finally, more applications of the new pattern are given. All GMC designs of 16 and 32 runs, a number of CMC designs of 64 runs, and some comparisons with the optimal designs under MA and CE criteria are tabulated.

• 出版日期2008-10
• 单位南开大学; 曲阜师范大学; 东北师范大学; 北京大学