A framework for fuzzy variable control charts with α-cuts


37th International Conference on Computers and Industrial Engineering 2007, Alexandria, Egypt, 20 - 23 October 2007, vol.1, pp.805-812 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 1
  • City: Alexandria
  • Country: Egypt
  • Page Numbers: pp.805-812
  • Keywords: α-cuts fuzzy R control chart, α-cuts fuzzy variable control charts, α-cuts fuzzy X control chart, α-level fuzzy midrange, Fuzzy variable control charts
  • Anadolu University Affiliated: Yes


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.