{"title":"加阶混合实验","authors":"Nicholas Rios, Dennis K. J. Lin","doi":"10.1080/00224065.2021.1960935","DOIUrl":null,"url":null,"abstract":"Abstract In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. Existing literature on mixture designs ignores the order of addition of the mixture components. This paper considers the Order-of-Addition (OofA) mixture experiment, where the response depends on both the mixture proportions of components and their order of addition. Empirical study demonstrates that if mixture-order interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. Full Mixture OofA designs are created which ensure orthogonality between mixture model terms and addition order effects. These designs allow for the estimation of (1) typical mixture model parameters and (2) order-of-addition effects. Moreover, models which include both main effects and key mixture-order interactions are introduced.","PeriodicalId":54769,"journal":{"name":"Journal of Quality Technology","volume":null,"pages":null},"PeriodicalIF":2.6000,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Order-of-addition mixture experiments\",\"authors\":\"Nicholas Rios, Dennis K. J. Lin\",\"doi\":\"10.1080/00224065.2021.1960935\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. Existing literature on mixture designs ignores the order of addition of the mixture components. This paper considers the Order-of-Addition (OofA) mixture experiment, where the response depends on both the mixture proportions of components and their order of addition. Empirical study demonstrates that if mixture-order interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. Full Mixture OofA designs are created which ensure orthogonality between mixture model terms and addition order effects. These designs allow for the estimation of (1) typical mixture model parameters and (2) order-of-addition effects. Moreover, models which include both main effects and key mixture-order interactions are introduced.\",\"PeriodicalId\":54769,\"journal\":{\"name\":\"Journal of Quality Technology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2021-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Quality Technology\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/00224065.2021.1960935\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, INDUSTRIAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Quality Technology","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/00224065.2021.1960935","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, INDUSTRIAL","Score":null,"Total":0}
Abstract In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. Existing literature on mixture designs ignores the order of addition of the mixture components. This paper considers the Order-of-Addition (OofA) mixture experiment, where the response depends on both the mixture proportions of components and their order of addition. Empirical study demonstrates that if mixture-order interactions exist, then the optimal mixture proportions identified by traditional models may be misleading. Full Mixture OofA designs are created which ensure orthogonality between mixture model terms and addition order effects. These designs allow for the estimation of (1) typical mixture model parameters and (2) order-of-addition effects. Moreover, models which include both main effects and key mixture-order interactions are introduced.
期刊介绍:
The objective of Journal of Quality Technology is to contribute to the technical advancement of the field of quality technology by publishing papers that emphasize the practical applicability of new techniques, instructive examples of the operation of existing techniques and results of historical researches. Expository, review, and tutorial papers are also acceptable if they are written in a style suitable for practicing engineers.
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