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The fuzzy set theory addresses the development of concepts and techniques for dealing with uncertainty or impression conditions. If the collected data from a process include vagueness due to human subjectively or measurement system, fuzzy control charts are available tools for monitoring and evaluating the process. The main contribution of fuzzy control charts is to provide flexibility to the control limits. When sample mean is too close to the control limits and the used measurement system is not so sensitive, the decision may be faulty. In this paper, the fuzzy standard deviation is firstly introduced to obtain fuzzy X and S control charts and then these fuzzy control charts are employed in food industry to monitor if the processes are under control or not. Additionally, the fuzzy X and S control charts are developed for the case that the population parameters are known.

The fuzzy regression control chart is a functional technique to evaluate the process in which the average has a trend and the data represents a linguistic or approximate value. In this study, the theoretical structure of the “α-level fuzzy midrange for α-cut fuzzy X -regression control chart” is proposed for triangular (TFN) and trapezoidal (TrFN) membership functions. In addition, the real world application is evaluated with fuzzy X regression control charts and fuzzy R control charts for the triangular membership function.