Design of EWMA and CUSUM Control Charts Based On Type-2 Fuzzy Sets

Abstract

A Shewhart control chart is a completely critical tool used for monitoring process’ stability. The superiority of EWMA and CUSUM control charts over Shewhart control charts is their ability to handle small process shifts. Although fuzzy sets can manage uncertainties related to processes, the extensions of fuzzy sets can be used to improve the ability of these control charts. The main advantage of type-2 fuzzy sets is that they can effectively model uncertainty even when the membership functions are not crisp. For these reasons, type-2 fuzzy sets are used to design of CUSUM and EWMA control charts. Therefore, in this study, the control limits and center lines in EWMA and CUSUM control diagrams have been re-formulated based on type-2 fuzzy sets. Furthermore, an illustrative example is provided to show the applicability of the proposed techniques.