First-Order Deletion Designs and the Construction of Efficient Nearly Orthogonal Factorial Designs in Small Blocks
提出一种通过构造高因子水平初步设计再删除多余处理组合来获得单重复不完全区组因子设计的方法，证明若初步设计正交则所得删除设计近正交且能高效估计低阶效应。
Abstract Single replicate factorial designs for incomplete block experiments are obtained by first constructing a single replicate preliminary design in incomplete blocks for the same number of factors but an excessive number of levels of the first factor, then deleting the excess treatment combinations to obtain a deletion design. Any single replicate preliminary design yields a single replicate deletion design. Furthermore, if the preliminary design is orthogonal, then the resulting deletion design is shown to be nearly orthogonal and, under certain reduced models, to provide efficient estimation of lower-order effects and in some cases an orthogonal analysis. For example, a 2×32 deletion design is constructed in three blocks of size 6, the 2 df confounded being the sum of interaction effects of F 2 and F 3 and second-order interaction effects. If second-order interactions are assumed negligible, then the deletion design provides efficient estimation of interactions between F 2 and F 3 and an orthogonal analysis. In another example, a 2×32 deletion design is constructed in nine blocks of size 2 with main effects of F 1 unconfounded. In a main-effects model, main effects of F 2 and F 3 are estimable with optimal average efficiency. Experimental settings involving more factor levels are also considered, tables are given showing the efficiency of the resulting deletion designs to compare favorably with optimal upper bounds, and the deletion designs are shown by comparison to be more efficient on lower-order effects than competing orthogonal designs.