In Statistical Process Control (SPC), both variable and attribute control charts are widely used techniques to monitor and evaluate the process with respect to the related quality characteristics. In variable control charts, quality characteristics are measured on a numerical scale, using two main parameters mean and standard deviation. When data are composed of individuals from a process, individual (X) control charts are used for mean and moving range (MR) control charts are used for standard deviation. Generally, the data in variable control charts are assumed to be composed of crisp values. But a measurement system including operator, gage, and environmental conditions may produce "uncertain" or "vague" data. In this case, the fuzzy set theory is an available tool for evaluating the vague data. In this study, fuzzy control limits for individual (X) and moving range (MR) control charts with alpha-cuts are constructed by using alpha-level fuzzy median transformation techniques. The real-world data are used and the process is evaluated by the developed fuzzy control charts.