均匀的三水平扩展设计

Uniform Three-level Extended Designs

以计算机技术为基础的模拟已被广泛应用于系统工程和高科技领域的发展中.计算机试验和设计已成为科技文献讨论的热点.扩展设计作为一种新型的试验设计近年来受到越来越广泛地关注.评价设计的最优性准则有很多,均匀性准则是其中的一种.均匀设计以其经济性和同时研究多个高水平因子时具有试验处理的灵活性被广泛接受,尤其是在对模型信息知之甚少时.本文以最优的U-型设计为基础,应用条件极值的方法讨论三水平扩展设计在三种常见偏差下的均匀性,得到了三水平扩展设计在三种常见偏差下的下界,该下界可作为寻找三水平均匀扩展设计的一个基准.

Simulation based on computer technology has been widely used in engineering and high-tech development. Design and modeling of computer experiments have been paid much attention in the literature. As a new type of experimental design, extended design has attracted more and more attention in recent years. There are many criteria for evaluating the optimal performance of the evaluation design, and the uniformity criterion is one of them. It is widely accepted especially in situations where little knowledge is known about the function to be modeled. Its practical success is due to its economical and flexible experimental runs to study many factors with high levels simultaneously. Based on the best U-type designs, the uniformity of three-level expansion designs under three kinds of common discrepancies is discussed by applying conditional extremnm in this paper. The lower bounds of the three- level extended designs under three common discrepancies are obtained, which can be used as a benchmark for finding the uniform three-level extended designs.