Optimality and Robustness to the Unavailability of Blocks in Block Designs
研究了从二元方差平衡不完全区组设计中移除t个等大小区组后所得设计的最优性，发现移除处理集不相交的区组得到最优设计，移除相同区组得到最差设计，并讨论了具有相同参数但不同支持大小的竞争设计的含义。
SUMMARY This paper investigates the optimality of designs derived from binary, variance-balanced incomplete block designs (BIBDs) by removing t equal-sized blocks which are not necessarily disjoint. It is shown that the optimal design is derived by removing blocks which have disjoint sets of treatments, and the worst design is derived by removing identical blocks. For BIBDs and t = 2 all resulting designs are ordered. The implication for competing BIBDs which have the same parameters v, b and k but different support sizes (numbers of distinct blocks) is addressed. Optimality and robustness are measured through the non-zero eigenvalues of the C-matrix of the design missing observations using the universal optimality criteria of Bondar.