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系統識別號 U0026-2906201716484900
論文名稱(中文) 多變量加權卜瓦松分佈管制圖之探討與研究
論文名稱(英文) Developing a New Control Chart for Multivariate Weighted Poisson Distribution
校院名稱 成功大學
系所名稱(中) 統計學系
系所名稱(英) Department of Statistics
學年度 105
學期 2
出版年 106
研究生(中文) 黃閔虹
研究生(英文) Min-Hung Huang
學號 R26044140
學位類別 碩士
語文別 中文
論文頁數 42頁
口試委員 指導教授-潘浙楠
口試委員-李俊毅
口試委員-鄭春生
中文關鍵字 多變量卜瓦松分配  計數型管制圖  瑕疵分數  平均連串長度 
英文關鍵字 Multivariate Poisson distribution  Attribute control chart  Demerit scheme  Average run length 
學科別分類
中文摘要 在產品製造過程中,為了監控產品品質特性之變化,必須藉由管制圖判斷製程之穩定性,以作為長期製程能力分析與製程改善之依據。隨著科技及工業的發展,公司或工廠在實際生產過程中所遇到的問題,常包含一個產品出現不同總類的瑕疵或各個瑕疵之間極可能彼此相互影響,此類狀況已無法使用傳統單變量的C或U等計數型管制圖來監控製程品質之狀態。
目前已有許多學者針對多變量卜瓦松管制圖進行發展及研究,如Chiu與Kuo (2008)、He et al.(2014)及Aslam et al.(2016)等人都曾提出相關的多變量卜瓦松管制圖之研究。但彼等所提出之多變量計數型管制圖時,並未對品質特性間之相關性進行探討,且未考慮各品質特性對產品影響程度之差異。因此,本研究根據不同品質特性之影響程度給予不同權重提出一個新的瑕疵分數統計量,並建立一個新的多變量加權卜瓦松管制圖(Multivariate Weighted Poisson control chart, WMP chart)。接著,我們使用平均連串長度(ARL)以模擬的方式來比較本研究所提出的WMP chart與Chiu與Kuo (2008)所建構的計數型多變量卜瓦松管制圖(Multivariate Poisson control chart, MP chart)之優劣,研究結果發現當多變量卜瓦松製程發生各種異常狀況時,WMP charts均較MP charts更能及早偵測到製程的偏移。最後,我們以Jiang et al.(2002)的電信通訊資料(telecommunication data set)為例進行數值實例驗證與說明,研究結果可供品管人員在未來監控多變量卜瓦松分配製程品質時之參考。
英文摘要 The SPC control charts play an important role in monitoring and improving the process quality. C charts and U charts are the most commonly used attribute control charts for detecting and removing assignable causes in a manufacturing process so that the process stability can be closely monitored. With the advent of modern technology and industry, different types of defects often appear in industrial products and those defects are likely to interact with each other. Thus, the traditional C charts and U charts can no longer be used for monitoring the process quality.
Many researchers had developed the control charts for multivariate Poisson distribution, such as Chiu and Kuo (2008), He et al.(2014) and Aslam et al.(2016). However, they did not consider the correlation among different quality characteristics and their degree of influence on the products. Thus, in this research, we propose a new statistic for demerit scheme, which gives different weights according to the degree of influence of the quality characteristics. Then, a new control chart for multivariate weighted Poisson distribution (WMP chart) is developed accordingly. Moreover, a simulation study is conducted to evaluate the detecting performances of our proposed WMP chart and multivariate Poisson control chart (MP chart) proposed by Chiu and Kuo (2008) using the out-of-control average run length (ARL1). Finally, a numerical example with a two dimensional telecommunication data set is given to demonstrate the usefulness of our proposed WMP chart. Both the simulation results and numerical example show that the detecting ability of our proposed WMP chart outperforms that of the MP chart when a process shift occurs. Hopefully, the results of this research can provide a better alternative for detecting the mean shifts occurred in a multivariate Poisson process.
論文目次 第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 2
第二章 文獻回顧與探討 4
2.1 傳統計數型管制圖 4
2.2 計數型資料之瑕疵分數 5
2.3 二變量卜瓦松分配 5
2.4 多變量卜瓦松管制圖 7
第三章 多變量加權卜瓦松管制圖之建構 10
3.1 多變量卜瓦松分配機率函數之建立與推導 10
3.2瑕疵分數統計量 10
3.3建構多變量加權卜瓦松管制圖 12
第四章 統計模擬分析 14
4.1 管制圖績效的評估 14
4.2 模擬設定 14
4.3 模擬結果 16
第五章 數值實例分析 22
5.1 資料介紹及參數估計 22
5.2 管制圖建構 23
第六章 結論與未來研究方向 27
6.1 結論 27
6.2 未來研究方向 28
參考文獻 29
附錄A 31
附錄B 42
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8. He, S., He, Z. and Wang, G.A., “CUSUM control charts for multivariate Poisson distribution.” Communications in Statistics – Theory and Methods, 43(6), 1192-1208. (2014)
9. Jiang, W., Au, S. T., Tsui, K. L. and Xie, M., “Process monitoring with univariate and multivariate c-charts.” Technical Report, The Logistics Institute, Georgia Tech, and The Logistics Institute-Asia Pacific. National University of Singapore. (2008)
10. Kemp, C. D. and Kemp , A. W., “Some properties of the ‘Hermite’ distribution.” Biometrika, 52(3/4), 381-394. (1965)
11. Kawamura, K., “The structure of bivariate Poisson distribution.” Kodai Mathematical Seminar Reports, 25(2), 246-256. (1973)
12. Kawamura, K., “The structure of multivariate Poisson distribution.” Kodai Mathematical Journal, 2(3), 337-345. (1979)
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14. Montgomery, D. C., Introduction to statistical quality control, 6th Ed., John Wiley & Sons, New York. (2009)
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16. Sandra G. B., Francisco A. and Eugenio K. E., “Optimal EWMA of linear combination of Poisson variables for multivariate statistical process control.” International Journal of Production Research, 53(14), 4141-4159. (2015)
17. Tahani C. M., “A new weighted rank coefficient of concordance.” Journal of Applied Statistics, 41(8), 1721-1745. (2014)
18. 蔡琬慈,加權卜瓦松分佈下計數型資料製程能力指標之研究,國立成功大學統計學研究所碩士論文。(2014)
19. 潘浙楠,品質管理:理論與實務(第三版),華泰文化,台灣。(2016)
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