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Complexity
Volume 2017, Article ID 4376809, 17 pages
https://doi.org/10.1155/2017/4376809
Research Article

Fuzzy and Control Charts: A Data-Adaptability and Human-Acceptance Approach

1Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, Kaohsiung 80778, Taiwan
2Office of Scientific Research, Lac Hong University, Dong Nai, Vietnam
3Department of Industrial Engineering and Management, Cheng Shiu University, Kaohsiung 83347, Taiwan
4Dong Nai Technology University, Dong Nai, Vietnam

Correspondence should be addressed to Dinh-Chien Dang; moc.liamg@79btkd.neihc

Received 11 October 2016; Revised 20 March 2017; Accepted 27 March 2017; Published 30 April 2017

Academic Editor: Thierry Floquet

Copyright © 2017 Ming-Hung Shu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For sequentially monitoring and controlling average and variability of an online manufacturing process, and 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 and 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’ and control-limits’ 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.