Split-plot designs with general minimum lower-order confounding  被引量:3

Split-plot designs with general minimum lower-order confounding

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作  者:WEI JiaLin 1,4,YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2,1 School of Mathematical Sciences and LPMC,Nankai University,Tianjin 300071,China 2 KLAS and School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China 3 School of Mathematical Sciences,Capital Normal University,Beijing 100037,China 4 School of Sciences,Tianjin University of Commerce,Tianjin 300134,China 

出  处:《Science China Mathematics》2010年第4期939-952,共14页中国科学:数学(英文版)

基  金:supported by National Natural Science Foundation of China (Grant No.10871104,10971107);the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No.20050055038)

摘  要:Split-plot designs have been widely used in industrial experiments.Up to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion.Recently,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et al.proposed a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory.It is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal designs.In this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot designs.Some comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.Split-plot designs have been widely used in industrial experiments.Up to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) criterion.Recently,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et al.proposed a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) theory.It is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal designs.In this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot designs.Some comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

关 键 词:FRACTIONAL FACTORIAL design GMC criterion minimum ABERRATION split-plot 

分 类 号:O212.6[理学—概率论与数理统计]

 

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