Fuzzy x̄ and s Charts: Left & Right Dominance Approach
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Traditionally, variable control charts are constructed based on precise data collected from well-defined quality characteristics of manufacturing products. However, in the real world, there are many occasions that the stated quality characteristic of products, such as surface roughness of optical lens, contains certain degree of imprecise information which is called fuzzy data. As a result, the traditional method for constructing the variable control charts exist a limitation of dealing with fuzzy data. Therefore, in this paper, x̄ and S control charts for fuzzy data are proposed. The fuzzy control limits are obtained on the basis of employing a well-known principle called resolution identity in the fuzzy theory. And in order to evaluate of the control charts, a fuzzy ranking method, named left and right dominance, is presented to classify the underlying manufacturing process condition. Finally, a practical example is provided to demonstrate the applicability of the proposed methodologies.
KeywordsFuzzy numbers Fuzzy control chart Left and Right Dominance
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