Abstract
There is much uncertainty and fuzziness in product quality attributes or quality parameters of a manufacturing process, so the traditional quality control chart can be difficult to apply. This paper proposes a fuzzy control chart. The plotted data was obtained by transforming expert scores into fuzzy numbers. Two types of nonconformity judgment rules—necessity and possibility measurement rules—are proposed. Through graphical analysis, the nonconformity judging method (i.e., assessing directly based on the shape feature of a fuzzy control chart) is proposed. For four different widely used membership functions, control levels were analyzed and compared by observing gaps between the upper and lower control limits. The result of the case study validates the feasibility and reliability of the proposed approach.
Highlights
International quality management expert Dr Juran pointed out that, for users, quality is the fitness for use, and not conformance to specification
This paper proposes a method to build a control chart based on fuzzy score number, and describes the design of nonconformity judging criteria and analysis of the type selection of fuzzy numbers
-cut of quality characteristic‐scoring sample fuzzy number, which isα denoted as a line segment judged abnormal when the -cut set fuzzy of sample fuzzywhich number and process fuzzy number do of quality characteristic-scoring sample number, is denoted as amean line segment connecting
Summary
International quality management expert Dr Juran pointed out that, for users, quality is the fitness for use, and not conformance to specification. Gülbay and Kahraman put forward a direct fuzzy approach in [1,2,3] They represented the linguistic variables and control limits of sample quality evaluation with a fuzzy set, without any defuzzification operation, and judged the process control state by the degree of overlap of α-cut set of sample fuzzy set and the control limits’ fuzzy set. The aforementioned literatures have provided good ideas to deal with the fitness quality attributes Their common feature is that they constructed fuzzy control charts by fuzzy operation and defuzzification based on fuzzy set membership functions given in advance. Literature that describes the construction of the fuzzy membership functions by use of rating scores, and subsequent creation of a corresponding fuzzy-number-based control chart, is still rare.
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