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系統識別號 U0026-0706201611322400
論文名稱(中文) 多變量管制圖在監控多階段系統製程品質上之應用研究
論文名稱(英文) A Study on Multivariate Control Charts for Monitoring and Controlling the Process Quality of Multistage Systems
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 104
學期 2
出版年 105
研究生(中文) 許竣幃
研究生(英文) Jun-Wei Hsu
學號 r26031066
學位類別 碩士
語文別 中文
論文頁數 49頁
口試委員 指導教授-潘浙楠
口試委員-鄭春生
口試委員-李俊毅
中文關鍵字 多階段系統  多變量線性迴歸模型  整體連串長度 
英文關鍵字 multistage manufacturing system  multivariate linear regression model  overall run length 
學科別分類
中文摘要 隨著現代科技進步與生活型態的改變,工業界多數的產品須經過多個階段的製程後,方能順利完成,並且這些製程常具有多個相關的品質特性。例如印刷電路板(print circuit board, PCB)、晶圓製造、汽車工業、航空工業、等許多製造領域之製程,皆屬多階段自相關製造系統之範疇。又鑒於上述高科技製程屬多重品質特性常具有自我相關的性質,若我們直接使用傳統的多變量管制圖來監控多重品質特性自我相關製程的處理方式並不恰當。近年來在品質學者們的努力下,已發展出殘差多變量指數加權移動平均(multivariate exponentially weighted moving average, MEWMA)管制圖、殘差多變量累和(multivariate cumulative sum, MCUSUM)管制圖等適合偵測自我相關製程微量變動的管制圖。由於傳統的統計製程管制(statistical process control, SPC)在監控與改進製程品質的方法上,通常僅針對單一階段具多重產品品質特性的製程品質進行監控與改善。Pan et al.(2016)提出監控多階段製程具單一產品品質特性之管制圖,但適合監控多階段系統製程品質的多變量管制圖仍付諸闕如。因此如何建構一個監控多階段系統具多重產品品質特性之多變量管制圖實有其必要性。
在考慮多階段製程的情況下,本研究先利用新的多變量線性迴歸模型(multivariate linear regression model)來描述跨階段製程的相關性,再利用各階段模型的殘差建構殘差MEWMA及MCUSUM管制圖。此外,本研究將以Pan et al.(2016)提出的整體連串長度(overall run length, ORL)作為各種多變量殘差管制圖偵測能力之評估與比較基準。
最後我們以一個級聯資料(cascade data)為例進行數值實例的驗證與說明,研究結果可提供實務工作者在監控多階段系統製程品質上之參考。
英文摘要 The study aims to develop a new control chart model suitable for monitoring the process quality of multistage manufacturing systems with multiple quality characteristics. Considering both the auto-correlated process outputs and the correlation occurring between neighboring stages in a multistage manufacturing system with multiple quality characteristics, we first propose a new multiple linear regression model to describe their relationship. Then, the multistage residual MEWMA and MCUSUM control charts are used to monitor the overall process quality of multistage systems. Moreover, an overall run length (ORL) concept is used to evaluate the detecting performances of our proposed multistage residual MEWMA and MCUSUM control charts. Finally, a numerical example with cascade data is used to illustrate the usefulness of our proposed multistage residual control charts. Hopefully, the results of this study can provide a better alternative for detecting process change and serve as a useful guideline for quality practitioners when monitoring and controlling the process quality of multistage systems with multiple quality characteristics.
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 3
第二章 文獻之回顧與探討 5
2.1 多階段系統 5
2.2 多階段系統的製程監控與改善 5
2.3 自我相關製程之管制圖 8
2.3.1 MEWMA管制圖 8
2.3.2 MCUSUM管制圖 9
第三章 多階段系統模型與多變量管制圖之建立 11
3.1 多階段系統模型的建立 11
3.2 多階段系統殘差管制圖之建立 14
3.2.1 多階段系統殘差MEWMA管制圖 14
3.2.2 多階段系統殘差MCUSUM管制圖 15
3.3 管制圖偵測效果評估標準之制定 16
3.3.1 整體連串長度合理性評估與機率分配之推導 16
3.4 多階段系統殘差MEWMA管制圖偵測能力之模擬分析 18
3.4.1 當多階段製程呈現穩定狀態下AOIRL值之選取 18
3.4.2 當多階段製程脫離管制狀態下AOORL值之比較 20
3.5 多階段系統殘差MCUSUM管制圖偵測能力之模擬分析 23
3.5.1 當多階段製程呈現穩定狀態下AOIRL值之選取 23
3.5.2 當多階段製程脫離管制狀態下AOORL值之比較 23
3.6 階段數對多階段系統管制圖 α 之敏感度分析 26
3.6.1 階段數對多階段系統MEWMA管制圖誤警率 α 之敏感度分析 26
3.6.2 階段數對多階段系統MCUSUM管制圖 α 之敏感度分析 29
3.7 品質特性數對多階段系統管制圖 α 之敏感度分析 31
3.7.1 品質特性數對多階段系統MEWMA管制圖誤警率 α 之敏感度分析 31
3.7.2 品質特性數對多階段系統MCUSUM管制圖誤警率 α 之敏感度分析 34
3.8 階段相關性對多階段系統管制圖 α 之敏感度分析 36
3.8.1 階段間相關性對多階段系統MEWMA管制圖誤警率 α 之敏感度分析 36
3.8.2 階段間相關性對多階段系統MCUSUM管制圖誤警率 α 之敏感度分析 38
第四章 數值實例分析 40
4.1 傳統Phase II MEWMA與多階段系統殘差MEWMA管制圖之比較 40
4.2 傳統Phase II MCUSUM與多階段系統殘差MCUSUM管制圖之比較 43
4.3 多階段系統殘差管制圖與傳統Phase II MEWMA與MCUSUM管制圖之比較 45
第五章 結論與未來研究之方向 46
5.1 結論 46
5.2 未來研究方向 46
參考文獻 48
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