{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:56:35Z","timestamp":1754157395871,"version":"3.41.2"},"reference-count":9,"publisher":"Emerald","issue":"3\/4","license":[{"start":{"date-parts":[[2009,4,10]],"date-time":"2009-04-10T00:00:00Z","timestamp":1239321600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009,4,10]]},"abstract":"<jats:sec><jats:title content-type=\"abstract-heading\">Purpose<\/jats:title><jats:p>The purpose of this paper is to extend two\u2010dimensional sequential uniform design and present three\u2010dimensional sequential uniform design which can optimize the problem of determining the extreme value of three\u2010factor polynomial.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Design\/methodology\/approach<\/jats:title><jats:p>Since there are limitations in two\u2010dimensional sequential uniform design, three\u2010dimensional sequential uniform design introduced in this paper is to arrange the experimental points by <jats:italic>U<\/jats:italic><jats:sub>9<\/jats:sub>(9<jats:sup>3<\/jats:sup>) uniform design table and to determine the maximum of the experimental values according to the demand. It is proven that the convergence of the experimental central point's sequence and that it can optimize the problem of determining the extreme value of no\u2010cross term quadratic polynomial monotone function class and the corresponding conditions are also proven. Taking the no\u2010cross term quadratic polynomial monotone function as an example, the superiority of it is testified.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>Three\u2010dimensional sequential uniform design can optimize the problem of determining the extreme value of three\u2010factor polynomial. It can get higher precision and better convergence but do fewer experiments than general uniform design.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Practical implications<\/jats:title><jats:p>A very effective method in resolving the problem of selecting optimum on multi\u2010dimensional space.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>A new method of three\u2010dimensional sequential uniform design which can get higher precision and better convergence is presented.<\/jats:p><\/jats:sec>","DOI":"10.1108\/03684920910944263","type":"journal-article","created":{"date-parts":[[2009,5,30]],"date-time":"2009-05-30T07:00:41Z","timestamp":1243666841000},"page":"542-548","source":"Crossref","is-referenced-by-count":1,"title":["Three\u2010dimensional sequential uniform design"],"prefix":"10.1108","volume":"38","author":[{"given":"Guizhi","family":"Wang","sequence":"first","affiliation":[]},{"given":"Jing","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Jibo","family":"Chen","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022031619425964600_b2","unstructured":"Fang, K.T. (1994), Uniform Design and Uniform Design Table, Beijing Science Press, Beijing."},{"key":"key2022031619425964600_b4","unstructured":"Fang, K.T. and Ma, C.X. (2002), Orthogonal and Uniform Design, Beijing Science Press, Beijing."},{"key":"key2022031619425964600_b6","unstructured":"Huang, X.\u2010Q. and Peng, J. (2005), \u201cThe validity of sequential \u03b2, c equidistant design for revolving monotone function\u201d, Application of Statistics and Management, Vol. 25 No. 4, pp. 37\u201041."},{"key":"key2022031619425964600_b1","unstructured":"Wand, L.\u2010L. and Wang, Z. (2005), \u201cSequential uniform design\u2010selecting optimum on multidimensional\u201d, Application of Statistics and Management, Vol. 25 No. 1, pp. 103\u20108."},{"key":"key2022031619425964600_b5","unstructured":"Wang, G., Zhao, J. and Chen, J. (2006), \u201cThe uniform design modeling and analysis based on least absolutes\u201d, Advances in Systems Science and Applications, Vol. 6 No. 4, pp. 699\u2010703."},{"key":"key2022031619425964600_b3","unstructured":"Wang, Y. and Fang, K.T. (1996), Application of Number Theoretic Methods in Statistical Analysis, Beijing Science Press, Beijing."},{"key":"key2022031619425964600_frd1","unstructured":"Kong, F., Zhang, G. and Wang, G. (2007), \u201cMartingale method of optimization design in investment and effectiveness model\u201d, Advances in Systems Science and Applications, Vol. 7 No. 1, pp. 1\u20106."},{"key":"key2022031619425964600_frd2","unstructured":"Wang, H., Cao, D. and Sun, J. (2005), \u201cMinimax method for a class nonsmooth global optimization problem\u201d, Advances in Systems Science and Applications, Vol. 5 No. 2, pp. 271\u20106."},{"key":"key2022031619425964600_frd3","unstructured":"Xu, C. (2003), \u201cHard and soft resolution approaches in optimisation\u201d, Analysis Advances in Systems Science and Applications, Vol. 3 No. 4, pp. 488\u201096."}],"container-title":["Kybernetes"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.emeraldinsight.com\/doi\/full-xml\/10.1108\/03684920910944263","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910944263\/full\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.emerald.com\/insight\/content\/doi\/10.1108\/03684920910944263\/full\/html","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,24]],"date-time":"2025-07-24T23:53:35Z","timestamp":1753401215000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.emerald.com\/k\/article\/38\/3-4\/542-548\/451326"}},"subtitle":[],"editor":[{"given":"Mian\u2010yun","family":"Chen","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2009,4,10]]},"references-count":9,"journal-issue":{"issue":"3\/4","published-print":{"date-parts":[[2009,4,10]]}},"alternative-id":["10.1108\/03684920910944263"],"URL":"https:\/\/doi.org\/10.1108\/03684920910944263","relation":{},"ISSN":["0368-492X"],"issn-type":[{"type":"print","value":"0368-492X"}],"subject":[],"published":{"date-parts":[[2009,4,10]]}}}