统计与数据科学学院知识库

试验设计是一门研究如何按照预定目标制定适当的试验方案，便于对试验结果进行有效统计分析的学科。它是数理统计学的一个分支，一个试验的设计需要考虑所要解决的问题，对试验结论做功效性、普遍性、耗资和耗时等方面的考量，选取适当的方法，从而给出试验实施的具体步骤和数据分析框架。

近些年来，混料试验设计成为了试验设计的主要研究方向之一。随着相关理论的丰富和发展，该领域已经取得了丰硕的成果，并且广泛的应用于工农生产、科学发展和社会实践中。混料设计目前主要在“最优”和“稳健”两个方向研究比较深入。而本文主要在前者多响应混料最优设计的基础上做三阶混料试验设计最优性的研究。通过将多响应混料模型向量化后得到单响应模型的思想，运用单响应混料模型的方法去解决最优设计的问题，同时结合最优设计的原理，得到信息矩阵的行列式，进而得到相应的数学表达式分别对参数求偏导获得最终数值结果。

Experimental design is a subject that studies how to formulate appropriate experimental scheme according to the predetermined target, which is convenient for effective statistical analysis of experimental results. It is a branch of mathematical statistics. The design of an experiment needs to consider the problems to be solved, consider the efficacy, universality, cost and time of the experimental conclusion, and select the appropriate method, so as to give the specific steps of the test implementation and the data analysis framework.

In recent years, mixing test design has become one of the main research directions of test design. With the enrichment and development of relevant theories, this field has achieved fruitful results, and has been widely used in industrial and agricultural production, scientific development and social practice. At present, mixtures design is mainly studied in two directions: "optimal" and "robust". In this paper, the optimization of the third order mixing test design is studied on the basis of the former multi-response optimal mixing design. By vectorizing the multi-response mixture model, the idea of single response mixture model was obtained. The method of single response mixture model was used to solve the problem of optimal design. At the same time, combining with the principle of optimal design, the determinant of information matrix was obtained, and then the corresponding mathematical expression was obtained.