Enhancing detectability of process variability in statistical process control under three-dimensional uncertainty: Evidence from textile industry

Although traditional statistical quality control (SQC) techniques, such as variable control charts (VCCs), are frequently used to monitor production processes, these methods may not be effective in dealing with the uncertainty and imprecision of data encountered in real-world production environments. For example, in textile manufacturing, maintaining high-quality standards is crucial to ensure consistent and reliable fabric products. This study presents an innovative approach by integrating picture fuzzy sets (PFSs) with one of well-known VCCs types named X-s charts to improve their sensitivity and robustness in identifying variations. As PFSs provide a more comprehensive way to represent uncertainty by incorporating positive, neutral, and negative membership degrees, they enable the creation of a more sensitive quality control method that accounts for both numerical data and subjective assessments. The proposed methodology first checks whether the data is normally distributed, which is an essential requirement for the reliability of the subsequent results. If normality is confirmed, the fuzzy center line (CL) and fuzzy control limits (CLs) are calculated, along with the distances from the center line to +16 and +26 values. These distances are used as inputs in a rule-based system that is suggested for VCCs in this paper, which enables categorizations such as "low degree in control" or "high degree out of control" providing a more detailed classification than traditional control charts. The proposed picture fuzzy X-s control charts is used to monitor variations in the shoulder-to-shoulder length in shirt manufacturing, demonstrating its effectiveness in distinguishing between in-control and out-of-control conditions, thereby offering a more flexible and insightful approach to process monitoring and decision-making in the textile industry.