Design of Fuzzy (u)over-tilde Control Charts

Abstract

When expressing any data in linguistic terms related to a quality characteristic, traditional statistical techniques are insufficient to capture the vagueness in the data. Linguistic data can be transformed into numerical values to handle them with traditional statistical techniques by using the fuzzy set theory. Fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive. The fuzzy set theory allows decision making with estimated values under incomplete or uncertain information. Classical Shewhart control charts monitor and evaluate the process as "in control" or "out of control". The fuzzy control charts additionally have the ability to consider linguistic or uncertain values and incorporate flexibility to the control limits. In this paper, the control charts of "fuzzy nonconformities per unit with alpha-cut" are developed. A real case application is given for the fuzzy nonconformities per unit in a truck engine manufacture.