Fuzzy regression control chart

Abstract

The fuzzy set theory is a powerful method to analyze the statistical data which includes ambiguity or vague comes from the structure of the process, measurement systems or environmental conditions. Crisp value collected process can transform the fuzzy numbers (a,b,c) by using the membership functions and calculate fuzzy control limits by using the traditional control limits equations. Thus, the flexibility on control limits can be achieved by analyzing the process like "in-control" or "out of control". The regression control chart is used especially to evaluate the tool wearing problem in industry. In the traditional regression control chart, all data assume crisp value. With fuzzy set theory, the fuzzy regression control chart can be handled based on a-cuts approach by using the fuzzy midrange transformation techniques. In this study, the theoretical structure of alpha-level fuzzy midrange for a-cuts for fuzzy X-regression control charts and fuzzy (R) over tilde control chart are proposed.