A framework for fuzzy variable control charts with ?-cuts

Abstract

In traditional variable control charts, center line, upper control limit and lower control limit are crisp values. In this situation, process are defined "in control" or "out of control" with depending on observation values because of the inflexible control limits. In many problems, control limits couldn't be so precise. Fuzzy set theory is inevitable tool for this uncertainty. Crisp control limits can be transformed to the fuzzy control limits by using membership functions. If one observation is too close to the control limits and the decision is given for process as "in control" or "out of control" according to this observation, related decision could be false. Fuzzy control limits provide more accurate evaluation for process. This study presents a framework fuzzy variable control charts that are fuzzy X and fuzzy R by the use of a-cut with numerical example. In this way, flexibility of control limits is achieved with fuzzy set theory.