Fuzzy rules for fuzzy $\overline{X}$ and $R$ control charts

Statistical process control ($SPC$), an internationally recognized technique for improving product quality and productivity, has been widely employed in various industries. $SPC$ relies on the use of control charts to monitor a manufacturing process for identifying causes of process variation and signaling the necessity of corrective action for the process. Fuzzy data exist ubiquitously in the modern manufacturing process, and in this paper, two alternative approaches to fuzzy control charts are developed for monitoring sample averages and range. These approaches are based on "fuzzy mode" and "fuzzy rules" methods, when the measures are expressed by non-symmetric triangular fuzzy numbers. In contrast to the existing fuzzy control charts, the proposed approach does not require the use of the defuzzification and this prevents the loss of information included in samples. A numeric example illustrates the performance of the method and interprets the results.