Abstract
Attribute control charts (ACCs) effectively evaluate the process’ situation based on nonconforming items (NCIs) and the defects status of items in the process. It is also clear that real case problems can include many uncertainties due to human evaluations and hesitancies, measurement systems errors, and process situations. The traditional control charts (CCs) that analyze process control situations need a major adjustment to take into account these uncertainties in these cases. For this aim, the fuzzy set theory (FST), a powerful tool for representing uncertainty by assigning membership functions, has been used successfully. Recently, some new fuzzy set extensions have been integrated into traditional CCs methods to represent the uncertainty more extensively and sensitively by involving other uncertainty parameters, such as non-membership and hesitancy functions. For this aim, one of these extensions, Pythagorean fuzzy sets (PFSs), which is a proper way of expressing uncertainty in the data and the hesitancy of the humans in the quality process, has been integrated with CCs to model the uncertainties of human evaluations together with their hesitancies and process’ uncertainties. Based on this perspective, in this paper, the well-known ACCs based on the total count of defects and NCIs called c, u, p, and np control charts, respectively, have been re-designed by using PFSs. Additionally, control situations of CCs have been deeply analyzed with respect to fuzzy limit values and measurements. Also, a rule-based approach that checks in-control and out-of-control situations regarding distance measurements is suggested to check the sample’s status more accurately. A decision process about the process control situation is presented based on PFSs to better represent of the process’ uncertainty that also includes humans-based evaluations. The proposed CCs based on PFSs have also been applied on a real case study from a manufacturing factory. The obtained results yield that the control charts based on PFSs have an ability to create accurate, sensitive and flexible results using the input data while analyzing the process’ stability.