Construction of Fuzzy Control Charts Based on Weighted Possibilistic Mean

Dabuxilatu Wang, Pinghui Li and Masami Yasuda

Communications in Statistics - Theory and Methods, 2014, vol. 43, issue 15, 3186-3207

Abstract: The problem of constructing control charts for fuzzy data has been considered in literature. The proposed transformation approaches and direct fuzzy approaches have their advantages and disadvantages. The representative values charts based on transformation methods are often recommended in practical application. For representing a fuzzy set by a crisp value, the weight of importance of the members assigned with some membership levels in a fuzzy set should be considered, and the possibility theory can be employed to deal with such problem. In this article, we propose to employ the weighted possibilistic mean (WPM), weighted interval valued possibilistic mean (WIVPM) of fuzzy number as a sort of representative values for the fuzzy attribute data, and establish new fuzzy control charts with WPM and WIVPM. The performance of the charts is compared to the existing fuzzy charts with a fuzzy c-chart example via newly defined average number of inspection for variation of control state.

Date: 2014
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DOI: 10.1080/03610926.2012.695852

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