Nearly Trend-Free Block Designs
当无趋势区组设计不存在时，提出近乎无趋势区组设计的概念和性质，并在线性和二次趋势下构造了完全区组设计，发现线性趋势下构造的设计是A和D最优的，二次趋势下可获得高效设计。
Abstract Trend-free block designs were developed to permit elimination of effects of low-order components of common within-block trends over experimental units. It is known that, for certain combinations of design parameters, trend-free block designs do not exist. In this article, concepts and properties of nearly trend-free block designs are presented in general, and complete block designs with linear or quadratic trends over plots within blocks are studied in particular. It is found that, under a linear trend, if trend-free complete block designs do not exist, nearly trend-free block designs can be constructed and they are A- and D-optimal. When the trend is quadratic, highly efficient designs can be obtained.