A design methodology based on two dimensional fuzzy linguistic variables for attribute control charts with real case applications

Abstract

Attribute control charts (ACCs) effectively evaluate process' situation based on nonconforming items (NCIs) and defects of items in a process. The traditional control charts (CCs) that analyze process control situations need a major adjustment to take into account uncertainties into eal case problems that can occur due to human evaluations and hesitancies, measurement systems errors, and process situations. The fuzzy set theory (FST) has been used successfully to reach this aim. Recently, some fuzzy set extensions have been integrated into traditional CCs to more extensively and sensitively model the uncertainty by involving other uncertainty parameters, such as non-membership value and hesitancy function. In this paper, one of these extensions, Pythagorean fuzzy sets (PFSs), has been adjusted with CCs to model the vagueness of human evaluations, their hesitancies, and uncertainties regarding the process. For this aim, the well-known ACCs based on the total count of defects and NCIs and called c, u, p, and np CCs, respectively, have been re-designed by using PFSs. Additionally, the control procedure of these CCs has been deeply analyzed with respect to fuzzy limit values and fuzzy 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. The proposed CCs based on PFSs have also been applied on a real case study from a manufacturing factory. The obtained results confirm that the CCs based on PFSs have an ability to create accurate, sensitive, and flexible results by using the input data while analyzing the process' stability.