均匀设计的等价原则及其构作

Uniformity equivalence principle and construction of uniform designs

从数据分析的角度,在换行、换列、换数码符号不改变均匀性的均匀等价原则条件下,定义了一种强度2的均匀设计(类似于正交设计)及一种超饱和的均匀设计———均匀差集矩阵(类似于差集矩阵),给出了一种用均匀差集矩阵及已知的强度2的正交设计构作新的强度2的均匀设计的方法.作为这个方法的应用,某些试验次数的强度2的混合水平均匀设计被构作出.

The unifomity of both the new uniform designs with strength 2 (similar to the orthogonal arrays with strength 2) and the supersaturated uniform designs-uniform difference matrices (similarly to the difference matrices in combinatorial theory) are investigated. The uniformity equivalence principle, which the uniformity of a uniform design is invariant by exchanging its any two rows or columns and its any two codes in each of columns, is based on data analysis. Using the uniform invariant, a generalized construction of uniform designs with strength 2 has been obtained by the uniform difference matrices and the orthogonal arrays with strength 2. As an application of the method, some new mixed-level uniform designs with strength 2 are constructed.