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. If the process is stable and statistically under control, it only displays a variation that is inherent to the process. Thus, 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 uncertainty, the traditional 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. When it comes to decisions made by quality engineers on the basis of their intuition, ordinary fuzzy sets cannot adequately represent the data. In such data, using Pythagorean fuzzy sets (PFSs), an extension of fuzzy sets, is a convenient way to represent not only the uncertainty in the data, but also the hesitations 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.