Construction of optimal supersaturated designs by the expansive replacement method

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY Journal of Statistical Planning and Inference Pub Date : 2023-11-10 DOI:10.1016/j.jspi.2023.106118

Hui Li , Liuqing Yang , Kashinath Chatterjee , Min-Qian Liu

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Abstract

Supersaturated design (SSD) plays an important role in screening factors. $E (f_{N O D})$ criterion is one of the most widely used criteria to evaluate multi-level and mixed-level SSDs. This paper provides some methods to construct multi-level $E (f_{N O D})$ optimal SSDs with general run sizes, which can also be extended to construct mixed-level SSDs. The main idea of these methods is combining two processed generalized Hadamard matrices with the expansive replacement method. These proposed methods are easy to perform. Besides, the non-orthogonality between any two columns of the resulting SSDs is well controlled by that of the source designs. Some illustrative examples are given and several new SSDs are provided in this paper.

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用膨胀置换法构造过饱和优化设计

过饱和设计(SSD)在筛选因素中起着重要的作用。E(fNOD)标准是评价多级和混合级ssd最常用的标准之一。本文提供了几种构造通用运行规模多级E(fNOD)最优ssd的方法，并可扩展到构造混合级ssd。这些方法的主要思想是将两个处理过的广义Hadamard矩阵与扩展替换法相结合。这些建议的方法易于执行。此外，所得到的ssd的任意两列之间的非正交性可以很好地由源设计的非正交性控制。文中给出了一些实例，并介绍了几种新型固态硬盘。

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来源期刊

Journal of Statistical Planning and Inference 数学-统计学与概率论

CiteScore

2.10

自引率

11.10%

发文量

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.