{"title":"Testing multiple dispersion effects from unreplicated order-of-addition experiments","authors":"Shin-Fu Tsai, Shan-Syue He","doi":"10.1111/anzs.12416","DOIUrl":null,"url":null,"abstract":"<p>Optimal addition orders of several components can be determined systematically to address order-of-addition problems when active location and dispersion effects are both taken into account. Based on the concept of fiducial generalised pivotal quantities, a new testing procedure is proposed in this paper to identify active dispersion effects from unreplicated order-of-addition experiments. Because the proposed method is free of all nuisance parameters indexed by the requirement set, it is capable of testing multiple dispersion effects. Simulation results show that the proposed method can maintain the empirical sizes close to the nominal level. A paint viscosity study is used to show that the proposed method can be practical. In addition, testable requirement sets are characterised when an order-of-addition orthogonal array is used to design an experiment.</p>","PeriodicalId":55428,"journal":{"name":"Australian & New Zealand Journal of Statistics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/anzs.12416","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Australian & New Zealand Journal of Statistics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/anzs.12416","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Optimal addition orders of several components can be determined systematically to address order-of-addition problems when active location and dispersion effects are both taken into account. Based on the concept of fiducial generalised pivotal quantities, a new testing procedure is proposed in this paper to identify active dispersion effects from unreplicated order-of-addition experiments. Because the proposed method is free of all nuisance parameters indexed by the requirement set, it is capable of testing multiple dispersion effects. Simulation results show that the proposed method can maintain the empirical sizes close to the nominal level. A paint viscosity study is used to show that the proposed method can be practical. In addition, testable requirement sets are characterised when an order-of-addition orthogonal array is used to design an experiment.
期刊介绍：
The Australian & New Zealand Journal of Statistics is an international journal managed jointly by the Statistical Society of Australia and the New Zealand Statistical Association. Its purpose is to report significant and novel contributions in statistics, ranging across articles on statistical theory, methodology, applications and computing. The journal has a particular focus on statistical techniques that can be readily applied to real-world problems, and on application papers with an Australasian emphasis. Outstanding articles submitted to the journal may be selected as Discussion Papers, to be read at a meeting of either the Statistical Society of Australia or the New Zealand Statistical Association.
The main body of the journal is divided into three sections.
The Theory and Methods Section publishes papers containing original contributions to the theory and methodology of statistics, econometrics and probability, and seeks papers motivated by a real problem and which demonstrate the proposed theory or methodology in that situation. There is a strong preference for papers motivated by, and illustrated with, real data.
The Applications Section publishes papers demonstrating applications of statistical techniques to problems faced by users of statistics in the sciences, government and industry. A particular focus is the application of newly developed statistical methodology to real data and the demonstration of better use of established statistical methodology in an area of application. It seeks to aid teachers of statistics by placing statistical methods in context.
The Statistical Computing Section publishes papers containing new algorithms, code snippets, or software descriptions (for open source software only) which enhance the field through the application of computing. Preference is given to papers featuring publically available code and/or data, and to those motivated by statistical methods for practical problems.
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