On the Optimality and Usage of Reinforced Block Designs for Comparing Test Treatments with a Standard Treatment
研究了强化区组设计的最优性，用于估计一组测试处理与标准处理的效果差异，以平均方差为最优性准则，并给出了SR设计的最优性条件及效率比较方法。
SUMMARY In this paper we consider the problem of determining optimal reinforced block designs for estimating the differences in effects between a set of test treatments of interest and some standard treatment. The optimality criterion considered is the average variance with which elementary treatment differences involving the standard treatment are estimated. A design is said to be reinforced with the standard treatment if each block of the design contains the standard treatment once, and we refer to such designs as SR-designs. Some sufficient conditions are derived for an SR-design to be optimal within the entire class of available SR-designs and some SR-designs which can be obtained by reinforcing each block of certain types of group divisible designs are shown to satisfy the conditions given. An efficiency criterion is also defined which can be used to compare arbitrary SR-designs with respect to how well they estimate treatment differences involving the standard treatment.