This paper gets some necessary conditions for the existence of some kinds of clear 4^m2^n compromise plans which allow estimation of all main effects and some specified two-factor interactions without assuming the remaining two-factor interactions being negligible. Some methods for constructing clear 4^m2^n compromise plans are introduced.
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.
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
In this paper, through an information-theoretic approach, we construct estimations and confidence intervals of Z-functionals involving finite population and with the presence of auxiliary information. In particular, we give a method of estimating the variance of finite population with known mean. The modified estimates and confidence intervals for Z-functionals can adequately use the auxiliary information, at least not worse than what the standard ones do. A simulation study is presented to assess the performance of the modified estimates for the finite sample case.
