Fuzzy process control based on fuzzy regression and possibility measures

The purpose of this paper is to present how a fuzzy process control chart is constructed for a process with fuzzy outcomes. In this paper, the fuzzy outcomes of the process are due to subjective quality ratings by experts. Fuzzy process control consists of an off-line stage and an on-line stage. In the off-line stage, experts give quality ratings of objects based on a numerical scale, and then these ratings are fuzzified as fuzzy numbers. Collective knowledge of experts in quality rating is acquired through fuzzy regression analysis. In the on-line stage, a computer vision system is set up to obtain the dimensions of objects, and then the fuzzy regression model maps these dimensions to fuzzy quality ratings in the form of fuzzy numbers. Finally, these fuzzy quality ratings are plotted on the fuzzy control chart. Out-of-control conditions are formulated based on possibility theory. This fuzzy control chart is analog to the x~ and R charts in statistical process control.