Process Incapability Analysis Under Uncertainty By Fermatean Fuzzy Perspective

Abstract

Process capability analysis (PCA) is widely used to evaluate whether processes can operate within specification limits (SLs). While traditional process capability indices (PCIs) emphasize capability, they often overlook incapability, which highlights deviations caused by inaccuracy and imprecision. The process incapability index (Cpp) offers a clear distinction in evaluating process precision and process accuracy, thereby providing a more comprehensive understanding of overall process performance. To extend this analysis, Fermatean fuzzy sets (FFSs) are employed because of their enhanced ability to represent uncertainty, vagueness, and hesitancy in experts’ judgments. To provide a more comprehensive perspective, this paper introduces a Fermatean fuzzy-based approach to the index Cpp. For this aim, a linguistic scale is developed to capture uncertainty in process parameters, and the index is demonstrated through an illustrative case on waiting times for electric vehicle charging stations. The results show that the proposed index based on FFSs has an ability to enable more flexible and sensitive evaluation compared with classical approaches, and more effective quality improvement strategies under uncertainty.