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研究生:湯淑惠
研究生(外文):Shu-Huei Tang
論文名稱:以類神經網路為基礎監控事件時間間隔數據之管制程序
論文名稱(外文):A Neural Network-based Process Control Procedure for TBE Data
指導教授:鄭春生鄭春生引用關係
學位類別:碩士
校院名稱:元智大學
系所名稱:工業工程與管理學系
學門:工程學門
學類:工業工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:中文
論文頁數:73
中文關鍵詞:事件時間間隔類神經網路CQC 管制圖CUSUM 管制圖EWMA 管制圖
外文關鍵詞:time-between-eventANNCQC chartCUSUM chartEWMA chart
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在統計管制製程中,通常利用傳統 c 管制圖來監控製程缺點率之變化。然而,在缺點率很低的高產出製程中,c 管制圖並無法滿足使用者所要求之統計特性。事件時間間隔管制圖 (time-between-events charts,簡稱 TBE 管制圖) 被認為是用來監控高產出製程的較佳方法。當製程的缺點率很低的情況下,TBE 管制圖比傳統計數值管制圖擁有較佳偵測製程異常之能力,並且更適合應用於線上即時監控系統。目前用來監控事件時間間隔數據之統計方法為:累積計量管制圖 (cumulative quantity control chart,簡稱 CQC 管制圖)、Exponential CUSUM 與 Exponential EWMA 管制圖。
本研究之主要目的為建構類神經網路之監控系統,以探討事件時間間隔數據之管制程序,並且利用平均連串長度作為衡量績效之評估指標。利用類神經網路監控服從指數分配之 TBE 數據,比較類神經網路與其他 TBE 管制圖之偵測績效。由於 TBE 數據為偏歪型的指數分配,除了使用 TBE 管制圖外,另一個監控 TBE 數據的方法即為數據轉換,以改善此種不對稱的資料型態。本研究加入數據轉換之前處理過程,使指數分配之數據能近似常態分配,期望能提升類神經網路監控 TBE 數據之績效。為了研究類神經網路之穩健性,將服從指數分配之 TBE 數據延伸至韋伯分配,期望類神經網路之偵測績效具有穩健性。研究顯示,類神經網路在偵測 TBE 數據擁有不錯之績效,並且在偵測服從韋伯分配之 TBE 數據具有穩健性。
In statistical process control, we usually use Shewhart c chart to monitor the defect rate. However, Shewhart c chart was shown to be inadequate to monitor the processes when the defect rate is extremely low. In order to provide a proper control scheme, the procedure of monitoring the time-between-events (TBE) data is suggested to be as an alternative to the traditional control charts. Instead of monitoring the number or the proportion of events occurring in a sampling interval, TBE charts focus on the time between the occurrences of events. There are several different ways in monitoring the TBE data, such as the Cumulative Quantity Control (CQC) chart, the exponential CUSUM, and the exponential EWMA control charts.
In this paper, we proposed a control technique based on the Artificial Neural Networks (ANN) for monitoring the TBE data. The TBE data is usually considered to follow an exponential distribution which is quite highly skewed. Three data transformation methods are also introduced in this research to make the statistics become more symmetric. Some performance comparisons between the ANN and the statistical control schemes are evaluated by the average run length (ARL) and the robustness of the ANN control procedure is also discussed. The results show the ANN monitoring system proposed in this research has superior performance than the statistical control charting techniques. And the robustness of the ANN is also established.
目錄
中文摘要 i
英文摘要 ii
致謝 iii
目錄 iv
表目錄 vi
圖目錄 vii
第一章 緒論 1
第二章 監控事件時間間隔數據之統計方法 8
2.1 TBE 管制圖 8
2.1.1 CQC 管制圖 9
2.1.2 Exponential CUSUM 管制圖 11
2.1.3 Exponential EWMA 管制圖 13
2.2 評估指標 15
第三章 事件時間間隔數據之轉換 17
3.1 數據轉換法 17
3.2 數據轉換後之統計特性分析 28
第四章 利用類神經網路發展監控事件時間間隔之管制程序 38
4.1 類神經網路 38
4.2 高產出製程之類神經網路監控系統 39
第五章 效益評估 49
5.1 類神經網路之績效評比 49
5.1.1 雙邊類神經網路 50
5.1.2 單邊類神經網路 53
5.2 數據轉換類神經網路之績效評比 62
5.3 類神經網路之穩健性分析 64
第六章 結論與未來研究 67
6.1 結論 67
6.2 未來研究 69
參考文獻 70

表目錄
表1. 三種數據轉換方式 29
表2. 轉換後 Y 值 I 與 I-MR 管制圖之 ARL 30
表3. 轉換後 Z 值 I 與 I-MR 管制圖之 ARL 32
表4. 轉換後 W 值 I 管制圖與 I-MR 管制圖之 ARL 33
表5. I管制圖中三種數據轉換之 ARL 35
表6. 比較三種數據轉換之統計量 36
表7. 訓練樣本之架構 45
表8. 數據轉換訓練樣本之架構 46
表9. 雙邊類神經網路與 CUSUM 之 ARL (ARLin=200) 51
表10. 雙邊類神經網路與 CUSUM 之 ARL (ARLin=370) 51
表11. 雙邊類神經網路與 CUSUM 之 ARL (ARLin=500) 52
表12. 左單邊類神經網路與 CUSUM 之 ARL (ARLin=200) 54
表13. 左單邊類神經網路與 CUSUM 之 ARL (ARLin=370) 55
表14. 左單邊類神經網路與 CUSUM 之 ARL (ARLin=500) 55
表15. 右單邊類神經網路與 CUSUM 之 ARL (ARLin=200) 57
表16. 右單邊類神經網路與 CUSUM 之 ARL (ARLin=370) 58
表17. 右單邊類神經網路與 CUSUM 之 ARL (ARLin=500) 58
表18. 類神經網路監控雙邊 TBE 數據 ARLin 固定為 250 61
表19. 數據轉換後類神經網路 ARL 之差異 62
表20. 類神經網路與 EWMA 管制法之 ARL 63
表21. 類神經網路與 CUSUM 之績效比較表 65

圖目錄
圖1. 二項分配圖 ( ) 2
圖2. 卜瓦松分配圖 ( ) 2
圖3. 時間加權之概念和比較 7
圖4. CQC 管制圖之管制統計量 9
圖5. CQC 之機率界限示意圖 ( ) 10
圖6. CQC 管制圖之ARL ( ) 16
圖7. 轉換後 Y 之直方圖 19
圖8. 轉換後 Z 之直方圖 23
圖9. 轉換後 W 之直方圖 26
圖10. 數據轉換之分佈曲線圖 28
圖11. I 與 I-MR 管制圖偵測 Y 值之 ARL 曲線圖 31
圖12. I 與 I-MR 管制圖偵測 Z 值之 ARL 曲線圖 32
圖13. I 與 I-MR 管制圖偵測 W 值之 ARL 曲線圖 34
圖14. 三種數據轉換之 ARL 曲線圖 35
圖15. 多層前饋網路之基本架構 40
圖16. 對數雙彎曲函數圖 41
圖17. 雙曲線正切函數圖 41
圖18. 多層前饋網路架構圖 42
圖19. 移動視窗之概念圖 44
圖20. 訓練樣本之建構方式 45
圖21. ARLin 為200 之雙邊 ARL 曲線 52
圖22. ARLin 為 200 之左單邊 ARL 曲線 56
圖23. ARLin 為 200 之右單邊 ARL 曲線 59
圖24. 韋伯分配之分佈圖 65
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