{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T07:48:27Z","timestamp":1767340107012,"version":"3.40.5"},"reference-count":47,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004663","name":"Ministry of Science and Technology of Taiwan","doi-asserted-by":"crossref","award":["MOST104-2221-E-151-018-MY3"],"award-info":[{"award-number":["MOST104-2221-E-151-018-MY3"]}],"id":[{"id":"10.13039\/501100004663","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2017]]},"abstract":"<jats:p>For sequentially monitoring and controlling average and variability of an online manufacturing process, <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mover accent=\"false\"><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:math> control charts are widely utilized tools, whose constructions require the data to be real (precise) numbers. However, many quality characteristics in practice, such as surface roughness of optical lenses, have been long recorded as fuzzy data, in which the traditional <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mover accent=\"false\"><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:math> charts have manifested some inaccessibility. Therefore, for well accommodating this fuzzy-data domain, this paper integrates fuzzy set theories to establish the fuzzy charts under a general variable-sample-size condition. First, the resolution-identity principle is exerted to erect the sample-statistics\u2019 and control-limits\u2019 fuzzy numbers (SSFNs and CLFNs), where the sample fuzzy data are unified and aggregated through statistical and nonlinear-programming manipulations. Then, the fuzzy-number ranking approach based on left and right integral index is brought to differentiate magnitude of fuzzy numbers and compare SSFNs and CLFNs pairwise. Thirdly, the fuzzy-logic alike reasoning is enacted to categorize process conditions with intermittent classifications between in control and out of control. Finally, a realistic example to control surface roughness on the turning process in producing optical lenses is illustrated to demonstrate their data-adaptability and human-acceptance of those integrated methodologies under fuzzy-data environments.<\/jats:p>","DOI":"10.1155\/2017\/4376809","type":"journal-article","created":{"date-parts":[[2017,4,30]],"date-time":"2017-04-30T17:01:22Z","timestamp":1493571682000},"page":"1-17","source":"Crossref","is-referenced-by-count":16,"title":["Fuzzy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>x<\/mml:mi><\/mml:mrow><mml:mo>-<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>s<\/mml:mi><\/mml:mrow><\/mml:math> Control Charts: A Data-Adaptability and Human-Acceptance Approach"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5866-6700","authenticated-orcid":true,"given":"Ming-Hung","family":"Shu","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, Kaohsiung 80778, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3413-4993","authenticated-orcid":true,"given":"Dinh-Chien","family":"Dang","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, Kaohsiung 80778, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8268-9854","authenticated-orcid":true,"given":"Thanh-Lam","family":"Nguyen","sequence":"additional","affiliation":[{"name":"Office of Scientific Research, Lac Hong University, Dong Nai, Vietnam"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bi-Min","family":"Hsu","sequence":"additional","affiliation":[{"name":"Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung 83347, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ngoc-Son","family":"Phan","sequence":"additional","affiliation":[{"name":"Dong Nai Technology University, Dong Nai, 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