Developing a fuzzy multivariate CUSUM control chart to monitor multinomial linguistic quality characteristics

Abstract

Currently, there are many situations in industry where simultaneous monitoring and control of two or more related quality characteristics of a product or a process becomes necessary. Independent monitoring of these kinds of quality characteristics can be very deceptive. Conventional multivariate control charts have been used to monitor and control the multivariate quality characteristics. However, these types of charts are not useful tools when the quality characteristics of a product or process are linguistic or fuzzy. Hence, fuzzy Hotelling’s T 2 chart (F-T 2) and fuzzy multivariate exponentially weighted moving average (F-MEWMA) control chart have been used to monitor these processes. In this paper, a fuzzy multivariate cumulative sum (F-MCUSUM) control chart is developed by means of the fuzzy set theory. Through a numerical comparison via a simulation study, the performance of the developed control approach is investigated on the basis of the average run length (ARL) in various out-of-control scenarios. When small shifts make the process out of control, the F-MCUSUM control chart is almost two times quicker than the F-T 2 and F-MEWMA control charts in detecting shifts. The results of numerical comparison indicate better performance of developed multivariate control approach in detecting small- and medium-sized shifts in the process. A case study in food industry is utilized to show the applicability of the proposed approach and the interpretation of the out-of-control signals.