用膨胀置换法构造过饱和优化设计

Pub Date : 2023-11-10 DOI:10.1016/j.jspi.2023.106118

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

{"title":"用膨胀置换法构造过饱和优化设计","authors":"Hui Li , Liuqing Yang , Kashinath Chatterjee , Min-Qian Liu","doi":"10.1016/j.jspi.2023.106118","DOIUrl":null,"url":null,"abstract":"<div><p>Supersaturated design (SSD) plays an important role in screening factors. <span><math><mrow><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>D</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> 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 <span><math><mrow><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>D</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> 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.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Construction of optimal supersaturated designs by the expansive replacement method\",\"authors\":\"Hui Li , Liuqing Yang , Kashinath Chatterjee , Min-Qian Liu\",\"doi\":\"10.1016/j.jspi.2023.106118\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Supersaturated design (SSD) plays an important role in screening factors. <span><math><mrow><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>D</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> 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 <span><math><mrow><mi>E</mi><mrow><mo>(</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>N</mi><mi>O</mi><mi>D</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> 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.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0378375823000873\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378375823000873","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Construction of optimal supersaturated designs by the expansive replacement method

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助