<p>Control charts are widely utilized in production to monitor product quality characteristics. Among them, variable control charts (VCCs) are designed for numerical data monitoring. However, these classical approaches often fall short when addressing processes that rely on human evaluations, as they fail to account for the vagueness and uncertainty inherent in human knowledge. This study aims to redesign VCCs by incorporating Pythagorean fuzzy sets (PFSs) to better address the indeterminacy and uncertainty of human evaluations based on Likert scales, particularly in quality control processes. PFSs were applied to develop VCCs for means and ranges, enabling the representation of human judgment uncertainty. A rule-based system was implemented to assess sample status by determining their position relative to control limits. The proposed method was validated using data from the evaluation of carcass quality. Applying PFS-based control charts demonstrated improved flexibility and sensitivity in human evaluation monitoring processes. The method outperformed other fuzzy extensions in a sensitivity analysis, confirming its robustness and practicality. Integrating PFSs into VCCs provides a powerful tool for managing uncertainty in human evaluations. This approach enhances the accuracy and adaptability of quality control processes, making it particularly useful for applications involving subjective assessments.</p>

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Design of variables control chart from linguistic terms based on Pythagorean fuzzy set approach with real case application

  • José L. Rodríguez-Álvarez,
  • Jorge L. García-Alcaraz,
  • José R. Díaz-Reza,
  • Cayetano Navarrete-Molina,
  • Iván González-Lazalde

摘要

Control charts are widely utilized in production to monitor product quality characteristics. Among them, variable control charts (VCCs) are designed for numerical data monitoring. However, these classical approaches often fall short when addressing processes that rely on human evaluations, as they fail to account for the vagueness and uncertainty inherent in human knowledge. This study aims to redesign VCCs by incorporating Pythagorean fuzzy sets (PFSs) to better address the indeterminacy and uncertainty of human evaluations based on Likert scales, particularly in quality control processes. PFSs were applied to develop VCCs for means and ranges, enabling the representation of human judgment uncertainty. A rule-based system was implemented to assess sample status by determining their position relative to control limits. The proposed method was validated using data from the evaluation of carcass quality. Applying PFS-based control charts demonstrated improved flexibility and sensitivity in human evaluation monitoring processes. The method outperformed other fuzzy extensions in a sensitivity analysis, confirming its robustness and practicality. Integrating PFSs into VCCs provides a powerful tool for managing uncertainty in human evaluations. This approach enhances the accuracy and adaptability of quality control processes, making it particularly useful for applications involving subjective assessments.