{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T08:44:13Z","timestamp":1762159453855,"version":"build-2065373602"},"reference-count":22,"publisher":"Wiley","issue":"8","license":[{"start":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T00:00:00Z","timestamp":1753747200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12301323","12131001"],"award-info":[{"award-number":["12301323","12131001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Quality &amp; Reliability Eng"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Screening designs are widely used to identify active effects from a large number of potential factors, ideally with a relatively small number of runs. This process is typically conducted in the early stages of experimentation. Orthogonal designs (ODs) are preferred because they allow the estimated main effects to remain uncorrelated. While two\u2010level and three\u2010level ODs have been extensively studied, ODs for mixed\u2010level experiments have received less attention. This is an important and timely issue, as mixed\u2010level experiments are common in practical applications. This paper proposes a new class of small mixed\u2010level ODs. These designs ensure the uncorrelated estimation of main effects and minimize run size among all ODs for a given number of factors. Additionally, the proposed designs exhibit favorable confounding patterns between main effects and two\u2010factor interactions, with each main effect being orthogonal to most two\u2010factor interactions. The construction methods leverage Paley's conference matrices. This research fills a critical gap in the literature by introducing new theoretical developments for mixed\u2010level\u00a0experiments.<\/jats:p>","DOI":"10.1002\/qre.70030","type":"journal-article","created":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T06:15:50Z","timestamp":1753856150000},"page":"3526-3533","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Small Mixed\u2010Level Orthogonal Designs"],"prefix":"10.1002","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-4149-0477","authenticated-orcid":false,"given":"Chunyan","family":"Wang","sequence":"first","affiliation":[{"name":"Center for Applied Statistics and School of Statistics Renmin University of China Beijing China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dennis K. J.","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Statistics Purdue University West Lafayette USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,7,29]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781119470007"},{"key":"e_1_2_7_3_1","first-page":"449","article-title":"The 2k\u2212p$2^{k-p}$ Fractional Factorial Designs","volume":"3","author":"Box G. E. 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