Fuzzy process control: construction of control charts with fuzzy numbers.

Chi-Bin Cheng∗

Department of Industrial Engineering and Management, Chaoyang University of Technology, Wufeng 413, Taiwan

Received 7 August 2003; received in revised form 1 March 2005; accepted 2 March 2005 Available online 23 March 2005

Abstract

This paper presents the construction of fuzzy control charts for a process with fuzzy outcomes derived from the subjective quality ratings provided by a group of experts. The proposed fuzzy process control (FPC) methodology comprises an off-line stage and an on-line stage. In the off-line stage, experts assign quality ratings to products based on a numerical scale. The individual numerical ratings are then aggregated to form collective opinions expressed in the form of fuzzy numbers. The collective knowledge applied by the experts when conducting the quality rating process is acquired through a process of fuzzy regression analysis performed by a neural network. In the on-line stage, the product dimensions are measured, and the fuzzy regression model is employed to automate the experts’ judgments by mapping the measured dimensions to appropriate fuzzy quality ratings. The fuzzy quality ratings are then plotted on fuzzy control charts, whose construction and out-of-control conditions are developed using possibility theory. The developed control charts not only monitor the central tendency of the process, but also indicate its degree of fuzziness. © 2005 Elsevier B.V. All rights reserved.

Keywords: Fuzzy process control; Fuzzy numbers; Possibility theory; Fuzzy regression analysis; Control charts

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