品質是競爭優勢的重要基礎，而供應商的品質管理更是影響產品品質、製程穩定性及供應鏈績效的重要環節。企業若能穩定取得符合品質要求之原物料，不僅可提升產品良率、降低生產成本，亦能建立穩定的供應合作關係，降低供應風險。因此，如何在兼顧品質保證、檢驗成本及決策效率下，有效評估供應商品質，已成為現代品質管理的重要課題。允收抽樣計畫因能以有限樣本推論整批產品品質，已廣泛應用於供應商品質管理，傳統重複允收抽樣計畫雖具有降低平均抽樣數之優點，但由於抽樣次數無上限，可能造成檢驗程序延長，增加品質管理成本與行政負擔，近年研究雖透過限制抽樣次數改善上述問題，然而現有方法多針對特定限制次數建立抽樣模型，當抽樣制度因不同品質需求或管理條件而調整時，往往需重新建立數學模型與設計抽樣計畫，限制了方法之延伸性與實務應用彈性。基於上述問題，本研究以製程能力指標𝑆𝑝𝑘 為品質衡量基礎，建立一套可適用於不同限制抽樣次數之一般化數學模型，使有限次數重複允收抽樣計畫不再侷限於特定抽樣制度，而能依不同品質需求進行設計與應用。同時，建立相對應之抽樣計畫設計方法，使抽樣制度兼顧品質保證、風險控制及檢驗成本，提升抽樣制度之設計效率與實務應用彈性。本研究透過實際案例驗證所建立模型之可行性，並與既有方法進行比較，以評估所提出方法於品質判定、抽樣效率及實務應用上的表現。研究成果可提供企業建立更具彈性與經濟效益之允收抽樣制度，作為供應商品質管理與品質決策之參考依據。

Quality serves as a critical foundation for competitive advantage, and supplier quality management is a vital link influencing product quality, process stability, and supply chain performance. Acceptance sampling plans are widely applied in supplier quality management due to their ability to infer the quality of an entire lot using a limited sample size. Although traditional repetitive acceptance sampling plans offer the advantage of reducing the average sample number, the lack of an upper limit on the number of sampling stages can prolong inspection procedures, increasing quality control costs and administrative burdens. To address these issues, recent studies have limited the maximum number of sampling stages; however, most existing methods develop sampling models tailored to specific restricted stages. When a sampling scheme needs adjustments due to varying quality requirements or managerial conditions, researchers must often reconstruct the mathematical models and redesign the sampling plans, which limits the scalability and practical flexibility of these methods. To address the aforementioned limitations, this study utilizes the process capability index 𝑆𝑝𝑘 as the quality measure to establish a generalized mathematical model applicable to varying limits on the number of sampling stages.

高枚妤. (2021). 藉由指標Spk評估供應商之允收抽樣計畫 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/ck9qc8
陳蕾雯. (2019). 利用Spk指標所要求樣本數來檢定供應商製程能力 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/pkvp7w
廖文寧. (2024). 以指標Spk建構有限次數之重複允收抽樣計畫 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/k9g6ba
褚耀聰. (2007). 依據製程能力指標Spk應用複式抽樣方法於供應商選擇 國立交通大學]. 臺灣博碩士論文知識加值系統. 新竹市. https://hdl.handle.net/11296/cj6k33
趙宸得. (2021). 使用製程能力指標建構有限抽樣次數之重複抽樣計劃 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/36k42s
劉怡良. (2023). 以製程能力指標建構限制重複抽樣次數之允收抽樣計畫 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/4u8en3
賴亮伃. (2023). 考量次數限制以指標Spk評估供應商之重複允收抽樣計劃 國立成功大學]. 臺灣博碩士論文知識加值系統. 台南市. https://hdl.handle.net/11296/8e4z2r
Aslam, M., Yen, C.-H., Chang, C.-H., & Jun, C.-H. (2013). Multiple states repetitive group sampling plans with process loss consideration. Applied MathematicalModelling,37(20),9063-9075.https://doi.org/https://doi.org/10.1016/j.apm.2013.04.020
Balamurali, S., Jeyadurga, P., & Usha, M. (2018). Determination of optimal quick switching system with varying sample size for assuring mean life under Weibull distribution. Sequential Analysis, 37(2), 222-234. https://doi.org/10.1080/07474946.2018.1466536
Boyles, R. A. (1991). The Taguchi Capability Index. Journal of Quality Technology, 23(1), 17-26. https://doi.org/10.1080/00224065.1991.11979279
Chan, L. K., Cheng, S. W., & Spiring, F. A. (1988). A New Measure of Process Capability: Cpm. Journal of Quality Technology, 20(3), 162-175.https://doi.org/10.1080/00224065.1988.11979102
Costa, A. F. B. (2023). Comparing the sequential and the repetitive Cpk sampling plans. Quality and reliability engineering international., 39(7), 2869-2880. https://doi.org/10.1002/qre.3395
Dodge, H. F. (1944). A Sampling Inspection Plan for Continuous Production. Journal of fluids engineering, 66, 127-133. https://doi.org/10.1115/1.4017953
Dodge, H. F. (1959). Sampling inspection tables : single and double sampling / Harold French and Harry G. Romig Dodge (2nd ed.). John Wiley.
Dodge, H. F. (1977). Chain Sampling Inspection Plan*. Journal of Quality Technology, 9(3), 139-142. https://doi.org/10.1080/00224065.1977.11980785
Dodge, H. F., & Romig, H. G. (1941). Single sampling and double sampling inspection tables. The Bell System Technical Journal, 20(1), 1-61. https://doi.org/10.1002/j.1538-7305.1941.tb00851.x
Gryna, F. M., Juran, J. M., & Bingham, R. S. (1974). Quality control handbook / J.M. Juran, editor-in-chief, Frank M. Gryna, Jr., associate editor, R.S. Bingham, Jr., associate editor (3rd ed.). McGraw-Hill.
Kane, V. E. (1986). Process Capability Indices. Journal of Quality Technology, 18(1), 41-52. https://doi.org/10.1080/00224065.1986.11978984
Lee, J., Hung, H.-N., Pearn, W., & Kueng, T. (2002). On the distribution of the estimated process yield index Spk. Quality and reliability engineering international., 18(2), 111-116. https://doi.org/10.1002/qre.450
Lin, C. J., & Pearn, W. L. (2010). Process selection for higher production yield based on capability index Spk. Quality and reliability engineering international., 26(3), 247-258. https://doi.org/10.1002/qre.1051
Montgomery, D. C. (2001). Introduction to statistical quality control / Douglas C. Montgomery (4th ed.). John Wiley.
Montgomery, D. C., & Jennings, C. L. (2009). Introduction to statistical quality control / Douglas C. Montgomery (6th ed.). Wiley.
Nesaee, M., & Fallah Nezhad, M. S. (2019). Designing variables sampling plans based on the yield index Spk. Communications in Statistics - Theory and Methods,50(3),507-520.https://doi.org/10.1080/03610926.2019.1639742
Pearn, W. L., Lin, G. H., & Chen, K. S. (1998). Distributional and inferential properties of the process accuracy and process precision indices. Communications in Statistics - Theory and Methods, 27(4), 985-1000. https://doi.org/10.1080/03610929808832139
Pearn, W. L., & Wu, C.-W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12-21. https://doi.org/https://doi.org/10.1016/j.omega.2005.01.018
Sherman, R. E. (1965). DESIGN AND EVALUATION OF A REPETITIVE GROUP SAMPLING PLAN. Technometrics, 7(1), 11. https://doi.org/10.2307/1266124
Tong, L.-I., & Chen, J.-P. (1998). 考慮製程能力指標之允收抽樣計劃. Journal of the Chinese Institute of Industrial Engineers, 15(1), 95-102. https://doi.org/10.1080/10170669.1998.10433362
Wu, C.-W., Pearn, W. L., & Kotz, S. (2009). An overview of theory and practice on process capability indices for quality assurance. International Journal of Production Economics, 117(2), 338-359. https://doi.org/https://doi.org/10.1016/j.ijpe.2008.11.008
Wu, C. W., Shu, M. H., Pearn, W. L., & Liu, K. H. (2008). Bootstrap approach for supplier selection based on production yield. International Journal of Production Research, 46(18), 5211-5230. https://doi.org/10.1080/00207540701278414
Yen, C.-H., Chang, C.-H., & Aslam, M. (2015). Repetitive variable acceptance sampling plan for one-sided specification. Journal of Statistical Computation and Simulation, 85(6), 1102-1116. https://doi.org/10.1080/00949655.2013.862791
Hsiang, T. C. and Taguchi, G. (1985). A tutorial on quality control and assurance-the Taguchi methods. ASA Annual Meeting, Las Vegas, Nevada.