Method for determining process capability indices for functional data

Abstract The increasing integration of sensors and data collection technologies in industrial environments has enabled more precise monitoring of process variables. In cases where the quality characteristic is better represented by a curve, such as the relationship between torque and RPM in electric motors, traditional control charts and capability indices may be insufficient. This study proposes a method for determining process capability indices based on functional data. Using real-world measurements from an industrial plant and theoretical specifications provided by a manufacturer, functional relationships were modeled through polynomial regression. Capability indices (Cp and Cpk) were then calculated along the entire explanatory variable domain, enabling a more comprehensive evaluation of process performance. The results indicate a high potential capability, though variability across the RPM range highlights the importance of localized assessments. The proposed method contributes to quality control practices in modern manufacturing, especially for processes governed by profile-type relationships.