Measuring the Variation of an Industrial Staple Manufacturing Process under 3-Dimensional Uncertainty Functions

In the context of industrial staple manufacturing, maintaining high-quality standards is essential to ensure product consistency and dependability. Traditional statistical quality control (SQC) methods, such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline{X}-s$</tex> control charts, are often employed to monitor and control these processes. However, these methods may fall short in handling uncertainty and imprecise data observed in real-world manufacturing environments. This study introduces a novel approach by integrating picture fuzzy sets (PFSs) into <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline{X}-s$</tex> variable control charts (VCCs) to enhance their sensitivity and robustness in detecting variations in the manufacturing process. Since PFSs, characterized by membership, non-membership, and hesitancy functions, provide a more comprehensive framework for representing uncertainty, we aim to establish a more sensitive method for quality control, accommodating both quantitative measurements and qualitative judgments by incorporating it. The proposed picture fuzzy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\overline{X}-s$</tex> control chart is applied to monitor mass variations in industrial staples, demonstrating their effectiveness in distinguishing in-control and out-of-control states, thereby offering a more flexible and informative approach to process monitoring and decision-making.