Performance Analysis and Computational Interface for <italic>X &#x2013; R</italic> Intuitionistic Fuzzy Control Chart

Abstract

Quality control, particularly through the use of control charts, has become essential in industry to ensure that processes free from special causes of variability. Many processes are subject to instrument uncertainty, human subjectivity, and operator hesitation at the time of measurement. In such cases, traditional control charts may not be as viable, so intuitionistic fuzzy control charts should be used, as they are able to represent the uncertainty and hesitation of the process. This study evaluates the performance of the $\bar {X}$ -R intuitionistic fuzzy control charts was measured by the Average Run Length (ARL), Standard Deviation Run Length (SDRL) and Run Length Percentiles. Additionally, computational interface was developed in the R programming language, using the Shiny package, capable of facilitating the user’s experience in combining the concepts presented. Different combinations of the $c_{L}$ and $c_{R}$ coefficients in the IF-WABL (Intuitionistic Fuzzy - Weigthed Average Based on Level) defuzzification method were considered, resulting in 17 scenarios. As these coefficients can be adjusted by the user, it is recommended that scenarios 4 to 7 be used for the general performance of the intuitionistic fuzzy $\bar {X}$ -R control chart, as they lead to reductions in ARL and SDRL values and percentiles close to those of the traditional control chart. A maximum reduction of 5.88% in ARL and 5.45% in SDRL was observed, both in scenario 4. This work showed that intuitionistic fuzzy control charts are efficient at detecting special causes, and that the computer interface developed is capable of performing the proposed functions.

Keywords

• Computational interface
• control chart
• hesitation
• intuitionistic fuzzy logic
• performance
• uncertainty