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Please use this identifier to cite or link to this item:
https://nccur.lib.nccu.edu.tw/handle/140.119/150303
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| Title: | 特定應用之多項比例監控
Monitoring Multinomial Proportions with Specific Applications |
| Authors: | 藍思皓
Lan, Szu-Hao |
| Contributors: | 蕭又新
楊素芬
Shiau, Yuo-Hsien
Yang, Su-Fen
藍思皓
Lan, Szu-Hao |
| Keywords: | 統計製程管制
EWMA管制圖
比例管制圖
多項式分配
二元常態分配
平均連串長度
Statistical Process Control
EWMA Control Chart
P chart
Multinomial Distribution
Bivariate Normal Distribution
Average Run Length |
| Date: | 2024 |
| Issue Date: | 2024-03-01 14:28:48 (UTC+8) |
| Abstract: | 管制圖在製造業中，管理流程品質非常重要。管制圖重要性在於能快速指出生產過
程中品質是否產生異常。持續監控流程品質變化，能夠確保製造業產品品質穩定。現有管制圖文獻大多假設單變量和多變量製程在統計管制下，數據呈現連續性。
本研究中，首先我們建立具有特定用途的 EWMA 多項式比例管制圖。我們使用兩 階段檢測方式來處理此問題:考慮 3 個比例下( p1, p2, p3 )，如果 p1 或 p2 發生變化，但 p1 和 p2 的總和維持不變，則組合後的管制圖不會顯示變化。模擬結果說明，我們的 p1 管制 圖可以快速檢測 p1 變化，並提供變化量 delta 大小。其次，我們探討從二元常態分配轉換到多項式分配，藉由每個品質變數規格界線，進而分類不同類型不良品比例。
Control charts are important in managing process quality in manufacturing.They are important because they can quickly indicate any changes in the quality of a production process. This constant monitoring of changes in process quality is essential for ensuring consistent and high-quality products in manufacturing. Much of the existing literature on control charts assumes that the data distribution follows a continuous pattern when both univariate and multivariate processes are in control.
In this research, firstly, we construct specified EWMA multinomial p charts that have particular uses. We utilize two-stage detection to approach the problem: consider triple proportions, ( p1, p2, p3 ), if p1 or p2 changes but the total of p1 and p2 stays the same, the combined chart doesn't show the change. The simulations suggest that our p1 chart can quickly detect changes in p1 and measure the magnitude of the change in delta. Secondly, we transform bivariate normal distribution to multinomial distribution and classify proportions by specification limits. |
| Reference: | Chen, G., Cheng, S. W., & Xie, H. (2001). Monitoring Process Mean and Variability with One EWMA Chart. Journal of Quality Technology, 33(2), 223-233. https://doi.org/10.1080/00224065.2001.11980069
Cozzucoli, P. C. (2009). Process Monitoring with Multivariate p-Control Chart. International Journal of Quality, Statistics, and Reliability, 2009, 707583. https://doi.org/10.1155/2009/707583
Gan, S., Yang, S.-F., & Chen, L.-P. (2023). A New EWMA Control Chart for Monitoring Multinomial Proportions. Sustainability, 15(15), 11797.
Jian Li , F. T. C. Z. (2014). Multivariate binomial/multinomial control chart. IIE Transactions, 46(5), 526-542. https://doi.org/10.1080/0740817X.2013.849830
Marcucci, M. (1985). Monitoring Multinomial Processes. Journal of Quality Technology, 17(2), 86-91. https://doi.org/10.1080/00224065.1985.11978941
Montgomery, D. C. (2012). Introduction to Statistical Control.
Montgomery, W. H. W. D. C. (2014). Some Current Directions in the Theory and
Application of Statistical Process Monitoring. Journal of Quality Technology, 46(1), 78-94. https://doi.org/10.1080/00224065.2014.11917955
Ryan, A. G., Wells, L. J., & Woodall, W. H. (2011). Methods for Monitoring Multiple Proportions When Inspecting Continuously. Journal of Quality Technology, 43(3), 237- 248. https://doi.org/10.1080/00224065.2011.11917860
Woodall, W. H. (1997). Control Charts Based on Attribute Data: Bibliography and Review. Journal of Quality Technology, 29(2), 172-183. https://doi.org/10.1080/00224065.1997.11979748 |
| Description: | 碩士
國立政治大學
統計學系
108354025 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0108354025 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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