隨著世代的變遷與市場需求的波動，生產者如何將現有的技術與製程提升，進而提高其在產業的核心競爭力是值得去深入探討的議題。挑選優良的供應商是生產管理上非常重視的一項課題，選擇合適的供應商可以增強公司的競爭力，對於公司的營銷和競爭力有著重大的影響，所以本研究針對供應商的製程能力選擇著手探討，將給定的製程能力指標，將允收抽樣的統計方法對供應商進行製程能力的評估，並計算出對應的允收抽樣檢驗貨批數、檢驗樣本數和判定標準，以確保供應商的製程能力是否滿足所要求的條件，運用已知的方法和工具對現有的流程架構加以改善並深入研究和分析，建構一套全新的方法，可以完整應用於實務方面。本研究運用供應商提供的樣本檢驗數據，經過計算與分析得到製程能力指標 Spk ，並加以討論製程能力指標 Spk 、樣本數與變異數三者之間的關聯性，發現指標 Spk 能夠在特定假設下，以更簡易的形式被運用在分析供應商的製程能力上。而在重複允收抽樣計劃的進行過程中，當樣本沒有足夠資訊證明該批量的品質特性是否落在要求的判定標準，則很有可能發生抽不完導致抽樣一直無法進行決策的情況，為改善重複允收抽樣計劃可能無法結束的狀況，於是本研究提出限制抽樣次數的改良，建立一個數學模型，使用演算法搜尋出最佳的目標函數，以更準確且有效率的指標判定供應商的製程能力，改善重複抽樣計劃的缺點並提升其績效。

This study utilizes sample inspection data provided by suppliers to calculate and analyze the process capability index Spk . The correlation between the process capability index Spk , sample size, and variance is discussed. It is found that the index Spk can be applied in a simpler form, under specific assumptions, to analyze the process capabilities of suppliers.

However, during the process of repeated acceptance sampling plans, if the samples do not provide sufficient information to determine whether the quality characteristics of the batch meet the required decision criteria, there is a high possibility of encountering situations where sampling cannot be completed, leading to a lack of decision-making.

To address the potential inability to conclude repeated sampling plans, this study proposes an improvement by introducing a limitation on the number of samplings. A mathematical model is established, and an algorithm is utilized to search for the optimal objective function, enabling a more accurate and efficient indicator to assess the suppliers' process capabilities, improving the drawbacks of repeated sampling plans and optimizing their performance.

Ahmad, L., Aslam, M., & Jun, C.-H. (2016). The design of a new repetitive sampling control chart based on process capability index. Transactions of the Institute of Measurement and Control, 38(8), 971-980.
Balamurali, S., & Aslam, M. (2019). Determination of multiple dependent state repetitive group sampling plan based on the process capability index. Sequential Analysis, 38(3), 385-399.
Balamurali, S., & Jun, C.-h. (2006). Repetitive group sampling procedure for variables inspection. Journal of Applied Statistics, 33(3), 327-338.
Boyles, R. A. (1991). The Taguchi capability index. Journal of Quality Technology, 23(1), 17-26.
Boyles, R. A. (1994). Brocess capability with asymmetric tolerances. Communications in Statistics-Simulation and Computation, 23(3), 615-635.
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.
Chou, Y.-M. (1994). Selecting a better supplier by testing process capability indices. Quality Engineering, 6(3), 427-438.
Heide, J. B., & Weiss, A. M. (1995). Vendor consideration and switching behavior for buyers in high-technology markets. Journal of Marketing, 59(3), 30-43.
Hsiang, T. C. (1985). A tutorial on quality control and assurance-the Taguchi methods. ASA Annual Meeting LA, 1985,
Jessenberger, J., & Weihs, C. (2000). A note on the behavior of Cpmk with asymmetric specification limits. Journal of Quality Technology, 32(4), 440-443.
Juran, J. M., Gryna, F. M., & Bingham, R. S. (1974). Quality Control Handbook (Vol. 3). McGraw-Hill New York.
Kane, V. E. (1986). Process capability indices. Journal of quality technology, 18(1), 41-52.
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.
Lee, Z. Y., & Pai, C. C. (2011). Operation analysis and performance assessment for TFT-LCD manufacturers using improved DEA. Expert Systems with Applications, 38(4), 4014-4024.
Lieberman, G. J., & Resnikoff, G. J. (1955). Sampling plans for inspection by variables. Journal of the American Statistical Association, 50(270), 457-516.
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.
Otsuka, A., & Nagata, F. (2017). Design method of Cpm-index based on product performance and manufacturing cost. Computers & Industrial Engineering, 113, 921-927.
Pearn, W., & Chen, K. (2002). One‐sided capability indices Cpu and Cpl: decision making with sample information. International journal of quality & reliability management.
Pearn, W., & Cheng, Y. C. (2007). Estimating process yield based on Spk for multiple samples. International Journal of Production Research, 45(1), 49-64.
Pearn, W., Lin, G., & Chen, K. (1998). Distributional and inferential properties of the process accuracy and process precision indices. Communications in Statistics-Theory and Methods, 27(4), 985-1000.
Pearn, W., Lin, G., & Wang, K. (2004). Normal approximation to the distribution of the estimated yield index Spk. Quality and Quantity, 38, 95-111.
Pearn, W., & Wu, C. H. (2013). Supplier selection for multiple-characteristics processes with one-sided specifications. Quality Technology & Quantitative Management, 10(1), 133-139.
Pearn, W., & Wu, C. W. (2007). An effective decision making method for product acceptance. Omega, 35(1), 12-21.
Pearn, W. L., Kotz, S., & Johnson, N. L. (1992). Distributional and inferential properties of process capability indices. Journal of Quality Technology, 24(4), 216-231.
Pearn, W. L., & Wu, C. W. (2006). Variables sampling plans with PPM fraction of defectives and process loss consideration. Journal of the Operational Research Society, 57(4), 450-459.
Perakis, M., & Xekalaki, E. (2016). On the relationship between process capability indices and the proportion of conformance. Quality Technology & Quantitative Management, 13(2), 207-220.
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.
Tseng, S. T., & Wu, T. Y. (1991). Selecting the best manufacturing process. Journal of Quality Technology, 23(1), 53-62.
Wu, C. H., Pearn, W., & Chuang, C. (2015). A powerful test for two-sided multiple independent characteristics supplier selection problem. Journal of Statistical Computation and Simulation, 85(4), 839-853.
Wu, C. W., Aslam, M., & Jun, C. H. (2012). Variables sampling inspection scheme for resubmitted lots based on the process capability index Cpk. European Journal of Operational Research, 217(3), 560-566.
Wu, C. W., Liu, S. W., & Lee, A. H. (2015). Design and construction of a variables multiple dependent state sampling plan based on process yield. European Journal of Industrial Engineering, 9(6), 819-838.
Wu, C. W., Pearn, W., & 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.
Wu, C. W., Shu, M., Pearn, W., & Liu, K. (2008). Bootstrap approach for supplier selection based on production yield. International Journal of Production Research, 46(18), 5211-5230.
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.