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On the basis of level permutation and mixture discrepancy, the average projection mixture discrepancy to measure the uniformity for low-dimensional projection designs is defined, the uniformity pattern and minimum projection uniformity criterion are presented for evaluating and comparing any asymmetric factorials. Moreover, lower bounds to uniformity pattern have been obtained, and some illustrative examples are also provided.<\/jats:p>","DOI":"10.3390\/axioms11120716","type":"journal-article","created":{"date-parts":[[2022,12,12]],"date-time":"2022-12-12T04:34:20Z","timestamp":1670819660000},"page":"716","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Projection Uniformity of Asymmetric Fractional Factorials"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0174-8945","authenticated-orcid":false,"given":"Kang","family":"Wang","sequence":"first","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3412-738X","authenticated-orcid":false,"given":"Zujun","family":"Ou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Jishou University, Jishou 416000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hong","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Zou","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1093\/biomet\/89.4.893","article-title":"Uniformity designs limit aliasing","volume":"89","author":"Hickernell","year":"2002","journal-title":"Biometrika"},{"key":"ref_2","first-page":"1066","article-title":"Generalized minimum aberration for asymmetrical fractional factorial designs","volume":"29","author":"Xu","year":"2001","journal-title":"Ann. 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Monte Carlo and Quasi-Monte Carlo Methods, Springer.","DOI":"10.1007\/978-3-642-56046-0"}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/12\/716\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:37:52Z","timestamp":1760146672000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/11\/12\/716"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,10]]},"references-count":26,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["axioms11120716"],"URL":"https:\/\/doi.org\/10.3390\/axioms11120716","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,10]]}}}