Charts Using Fuzzy Trapezoidal Number

Statistical Process Control (SPC) is used to monitor the process stability which ensures the predictability of the process. In 1920‟s Shewhart introduced the control chart techniques that are one of the most important techniques of quality control to detect if assignable causes exist. The widely used control chart techniques are R X  and S X  . These are called traditional variable control charts. A traditional variable control chart, consists of three lines namely Center Line, Upper Control Limit and Lower Control Limit. These limits are represented by the numerical values. The process is either “in-control” or “out-of-control” depending on numerical observations. For many problems, control limits could not be so precise. Uncertainty comes from the measurement system including operators and gauges and environmental conditions. In this situation, fuzzy set theory is a useful tool to handle this uncertainty. Numeric control limits can be transformed to fuzzy control limits by using membership functions. If a sample mean is too close to the control limits and the used measurement system is not so sensitive, the decision may be faulty. Fuzzy control limits provide a more accurate and flexible evaluation. In this paper, the fuzzy  cut R X ~ ~  and S X ~ ~  control charts are constructed by using fuzzy trapezoidal numbers. An application is presented for the proposed fuzzy R X ~ ~  control charts.