Proposed α-cut CUSUM and EWMA Control Charts for Fuzzy Response Observations

Abstract

This research proposesalpha ([Formula: see text]-cut Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts with fuzzy response observations in a manufacturing process under the existence of mean shift utilizing the fuzzy logic. In this research, the replicate’s observation is a fuzzy number represented by a triangular membership function, with the lower, average, and upper observation values. The fuzzy numbers are then normalized and assigned as input to the fuzzy logic, while a common output measure (COM) value is the output. Finally, the original values of the COM values are employed in developing the EWMA and CUSUM control charts with different [Formula: see text]-cut values. Three real case studies are adopted to illustrate the proposed EWMA and CUSUM control charts; including piston inside diameter, cap’s angel, and tablet weight. Results showed that the proposed EWMA and CUSUM control charts efficiently monitor fuzzy observations and detect the shift in process means. Moreover, the amount mean shift and [Formula: see text]-cut values affect the decision on process condition. In conclusion, the proposed approach is found effective in monitoring quality characteristic of fuzzy observations under mean shift which can be applied in a wide range of business applications.