Design of variable control charts based on type-2 fuzzy sets with a real case study

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Control charts (CCs) are very effective tools to follow process variation and to improve process quality. It is completely critical to increase the sensitiveness and flexibility of CCs to gain a deeper perspective for process control. When constructing conventional CCs, errors may occur due to operator or measuring instruments in performing the measurement. By the way, some data related to CCs can include “uncertainty” or “vagueness” related to process and human evaluations or inspector judgments. We know that classical CCs cannot be able to manage this process. The fuzzy set theory (FST) is one of the most important tools to solve these problems, and the CCs designed based on FST are more usable and preferable for monitoring the process. By the way, one of the extensions of FST named type-2 fuzzy sets that have fuzzy membership degrees is more capable of modeling uncertainty. Therefore, they can be successfully used to the design of the control process in a more flexible and sensitive way. In this paper, the type-2 fuzzy sets have been used to the design of variable control charts to increase the precision and flexibility of them. For this aim, $$\bar{x} - R$$ , $$\bar{x} - S$$ and $$I - MR$$ control charts have been re-designed by using type-2 fuzzy sets. Additionally, these charts have been applied on a real case application from electronic industry, and the obtained results indicate that CCs based on type-2 fuzzy sets can evaluate the process in a more sensitive and flexible way.