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系統識別號 U0026-2406201915593300
論文名稱(中文) 加權卜瓦松分佈下多變量製程能力指標制定之研究
論文名稱(英文) Developing Process Capability Index 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 107
學期 2
出版年 108
研究生(中文) 李郡安
研究生(英文) Chun-An Lee
學號 R26064019
學位類別 碩士
語文別 中文
論文頁數 36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 製程能力指標  多變量卜瓦松分配  瑕疵分數 
英文關鍵字 process capability index  multivariate Poisson distribution  demerit scheme 
學科別分類
中文摘要 一般而言,統計製程管制係以製程能力分析監控製程的品質是否符合工程規格或達到客戶要求的水準,而製程能力指標常用於評估製程的風險。
  本研究的目的係針對一個多變量卜瓦松製程,在考量品質特性間之相關性及各品質特性對產品影響程度不同情況下,提出一個能正確反映製程風險的新計數型製程能力指標。首先,假設一製程包含q個品質特性,而這q個品質特性之瑕疵數係服從多變量卜瓦松分配。我們藉由瑕疵分數統計量Dw來評估瑕疵數對於製程造成的風險,並利用望小特性下非常態製程能力指標之概念提出新的製程能力指標Cw。
  接著,我們以數值計算方式評估比較在不同相關係數下當製程平均發生偏移時,各種製程能力指標之表現。結果發現無論在何種相關係數或權重改變之情形下,本研究提出之新製程能力指標Cw皆可正確合理的反映出瑕疵數對於製程所造成的風險。最後,我們以Jiang等(2002)所使用之電信通訊資料及長春化工絕緣紙汙點之嚴重程度為例進行數值實例驗證,說明我們提出之新製程能力指標Cw較能合理反映瑕疵數對多變量卜瓦松製程造成的風險,研究結果可供品管人員未來在評估計數型多重品質特性製程風險時之參考。
英文摘要 Process capability analysis (PCA) is frequently employed by manufacturers to evaluate whether the capability of process can meet the customer’s requirement or not. Practically, process capability indices (PCIs) are often used for assessing the manufacturing risk in most industries.
This paper aims to propose a new attribute process capability index by considering the correlation among different defect types and their degrees of influence on the final product for multivariate Poisson processes. Considering a process has q quality characteristics and the number of defects or q quality characteristics follows a multivariate Poisson distribution, we use the statistic of demerit scheme Dw to measure the risk of number of defects for a multivariate Poisson process. Then, the new process capability index Cw for the statistic Dw can be defined by adopting the concept of non-normal PCIs for the Smaller-the-better (STB) case.
In the numerical analysis, we compare the performance of various PCIs under different coefficients when process mean shifts occurred. The simulation results show that our proposed attribute process capability index can properly reflect the manufacturing risk of a multivariate Poisson process when different weights are assigned to the associated quality characteristics. Finally, two numerical examples with telecommunication data set mentioned in Jiang et al.(2002) and the black spots problem occurred in the insulation paper at Chang Chung Company are used to demonstrate the usefulness of our proposed capability index Cw.
論文目次 目錄
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 瑕疵分數 4
2.2 多變量加權卜瓦松分配 4
2.3 計量型製程能力指標 6
2.4 非常態製程能力指標 7
2.5 計數型製程能力指標 9
第三章 加權卜瓦松分佈下多變量製程能力指標之制定 11
3.1 加權卜瓦松分佈下多變量製程能力指標之制定 11
3.2 加權卜瓦松分佈下多變量製程能力指標之數值計算 14
第四章 數值實例分析 26
4.1 二維電信通訊資料 26
4.2 台灣長春化工資料 27
第五章 結論與未來研究方向 30
5.1 結論 30
5.2 未來研究方向 31
參考文獻 32
附錄A 35

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