{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T23:19:54Z","timestamp":1771543194293,"version":"3.50.1"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T00:00:00Z","timestamp":1580688000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"MOST","doi-asserted-by":"publisher","award":["MOST-108-2221-E-468-003"],"award-info":[{"award-number":["MOST-108-2221-E-468-003"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>During the development of fan products, designers often encounter gray areas when creating new designs. Without clear design goals, development efficiency is usually reduced, and fans are the best solution for studying symmetry or asymmetry. Therefore, fan designers need to figure out an optimization approach that can simplify the fan development process and reduce associated costs. This study provides a new statistical approach using gray relational analysis (GRA) to analyze and optimize the parameters of a particular fan design. During the research, it was found that the single fan uses an asymmetry concept with a single blade as the design, while the operation of double fans is a symmetry concept. The results indicated that the proposed mechanical operations could enhance the variety of product designs and reduce costs. Moreover, this approach can relieve designers from unnecessary effort during the development process and also effectively reduce the product development time.<\/jats:p>","DOI":"10.3390\/sym12020227","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Application of Gray Relational Analysis and Computational Fluid Dynamics to the Statistical Techniques of Product Designs"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5518-4669","authenticated-orcid":false,"given":"Hsin-Hung","family":"Lin","sequence":"first","affiliation":[{"name":"Department of Creative Product Design, Asia University, Taichung City 41354, Taiwan"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jui-Hung","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Mold and Die Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chi-Hsiung","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Creative Product Design, Asia University, Taichung City 41354, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"846","DOI":"10.1016\/j.applthermaleng.2005.09.020","article-title":"Numerical investigation of fan performance in a forced draft air-cooled steam condenser","volume":"26","author":"Bredell","year":"2006","journal-title":"Appl. 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