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                A Model for Evaluating and Analyzing Process Capability in Multi-Quality-Characteristic Products            
            
                                by
                    
    Kuen-Suan Chen
 Kuen-Suan Chen
Kuen-Suan Chen
    Chien-Hsin Cheng
 Chien-Hsin Cheng
Chien-Hsin Cheng
    Chia-Pao Chang
 Chia-Pao Chang
Chia-Pao Chang
    Kai-Chao Yao
 Kai-Chao Yao
Kai-Chao Yao and
 and 
    Chun-Min Yu
 Chun-Min Yu
Chun-Min Yu
                
                    
                            1
                        Department of Industrial Engineering and Management, National Chin-Yi University of Technology, Taichung 411030, Taiwan
         
                    
                            2
                        Department of Business Administration, Chaoyang University of Technology, Taichung 413310, Taiwan
         
                    
                            3
                        Institute of Innovation and Circular Economy, Asia University, Taichung 413305, Taiwan
         
                    
                            4
                        Department of Electrical and Mechanical Technology, National Changhua University of Education, Changhua 50074, Taiwan
         
    
    
            
            *
            Authors to whom correspondence should be addressed. 
         
    
    
    
 
             
            
                Mathematics 2025, 13(21), 3467; https://doi.org/10.3390/math13213467 (registering DOI)
            
            
                    
    Submission received: 23 September 2025
    /
    Revised: 18 October 2025
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    Accepted: 28 October 2025
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    Published: 30 October 2025
            
                
    
            
            
                        
            
            
            
        
                        
        
                        
        
                        
        
        
                        
        
                        
                                                                            
                                                                            
            
                            Abstract
            
            
                                                            A segment of the machine tool industry in Taiwan specializes in manufacturing equipment tailored to the semiconductor sector. Due to the stringent quality requirements inherent in semiconductor manufacturing processes, the machine tools employed in these processes are also subject to correspondingly rigorous quality standards. In fact, a machine tool is assembled from hundreds of individual components, each of which must meet the required standards to ensure that the final product adheres to overall quality requirements. Similarly, each component possesses multiple quality characteristics, all of which must individually satisfy the specified criteria to guarantee that the component achieves the required quality level. Clearly, without a comprehensive evaluation model, ensuring final product quality is difficult. To address this practical issue, this study employed the Process Capability Index (PCI), the most widely used process capability index in the industry, and based on statistical verification principles, constructed a quality assessment and analysis model applicable to products with multiple quality characteristics. This approach enables process engineers to simultaneously evaluate all product quality characteristics and determine whether they meet the desired quality standards. For products that do not meet the expected quality standards, improvement directions are proposed, and improvement decisions are made based on cost and economic benefits, thereby ensuring final product quality. This study concludes with a real-world case study to illustrate the application of the proposed model, making it easier for relevant industries to apply the model.
                    
                            
            
                            
            
                        
                        
                        
                    
                        
            
            
    
        
     
            
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MDPI and ACS Style
                    Chen, K.-S.;                     Cheng, C.-H.;                     Chang, C.-P.;                     Yao, K.-C.;                     Yu, C.-M.    
        A Model for Evaluating and Analyzing Process Capability in Multi-Quality-Characteristic Products. Mathematics 2025, 13, 3467.
    https://doi.org/10.3390/math13213467
    AMA Style
    
                                Chen K-S,                                 Cheng C-H,                                 Chang C-P,                                 Yao K-C,                                 Yu C-M.        
                A Model for Evaluating and Analyzing Process Capability in Multi-Quality-Characteristic Products. Mathematics. 2025; 13(21):3467.
        https://doi.org/10.3390/math13213467
    
    Chicago/Turabian Style
    
                                Chen, Kuen-Suan,                                 Chien-Hsin Cheng,                                 Chia-Pao Chang,                                 Kai-Chao Yao,                                 and Chun-Min Yu.        
                2025. "A Model for Evaluating and Analyzing Process Capability in Multi-Quality-Characteristic Products" Mathematics 13, no. 21: 3467.
        https://doi.org/10.3390/math13213467
    
    APA Style
    
                                Chen, K.-S.,                                 Cheng, C.-H.,                                 Chang, C.-P.,                                 Yao, K.-C.,                                 & Yu, C.-M.        
        
        (2025). A Model for Evaluating and Analyzing Process Capability in Multi-Quality-Characteristic Products. Mathematics, 13(21), 3467.
        https://doi.org/10.3390/math13213467
    
 
                 
                                    
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