Design of Control Charts for Number of Defects Based on Pythagorean Fuzzy Sets

Abstract

Control charts (CCs) are completely useful techniques to monitor the process’ stability and control. If the process is stable and in statistical control, it only displays a variation that is inherent to the process. So, usage of them is completely critical for the process’ improvements. Two types of attribute control charts (ACCs) are related to the total count of defects that are the designs of the non--measurable characteristics and they are called $u$ and $c$ control charts. If the process related to evaluations about defects includes some uncertainty, the ACCs are insufficient to reflect the available data in design stages. The fuzzy set theory (FST) is a tool for representing uncertainty by assigning membership functions. In case of quality engineers' intuitive behaviours, ordinary fuzzy sets are incapable of the representation of the data. In this type of data, Pythagorean fuzzy sets (PFSs), which is an extension of FST is a proper way of representing not only uncertainty in the data but also hesitancy of the quality engineers. Through that, in this paper, the design of control charts for the number of defects based on PFSs has been proposed. An extension of $u$ and $c$ control charts based on PFSs are constructed and the design of these control charts has been detailed. Moreover, a descriptive example is introduced to check the applicability of the proposed method.

Keywords

• c control chart
• Fuzzy logic
• Pythagorean fuzzy sets
• u control chart

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