臺灣博碩士論文加值系統

製程人員持續地在改善製程，而改善製程的必要步驟之ㄧ，即是有效地辨識出製程產生干擾時的改變點或啟始點，若能儘早找出製程失控啟始點，便可減少因延後找出製程失控根本原因所造成人力與資源的浪費。因而，如何有效地估計出製程干擾啟始點是一個非常重要的研究課題。不同於傳統常態製程假設，本文探討當製程服從Gamma分配時，如何使用X_bar與S管制圖結合最大概似估計法，以估計Gamma製程的改變點，本文並且驗證所提出的參數估計量具有不偏與一致性的統計性質。由於應用X_bar之傳統SPC管制界限監控Gamma製程會產生假警訊，本文以理論推導出X_bar管制圖監控Gamma製程時之真實管制界限，本文並應用蒙地卡羅技術決定S管制圖之管制界限；同時，本文將藉由模擬範例展示本研究方法之優異成效。

The process personnel always seek the opportunity to improve the processes. One of the essential steps for process improvement is to quickly estimate the starting time or the change point of a process disturbance. If we can promptly recognize a disturbance in a process, we will be able to fix the root causes of the problem and significantly improve the underlying process. Consequently, how to effectively estimate the starting time of a disturbance becomes a very important research issue.
Different from the traditional normally distributed assumption for a process, this study considers a process which follows a gamma distribution. This study proposes a fruitful approach to estimate the starting time of a disturbance for gamma processes. This study demonstrates that the proposed estimators are unbiased and consistent estimators. The proposed approach combines the commonly used X_bar control chart and S control charts and the maximum likelihood (ML) technique. In addition, when we apply the typical X_bar to monitor the gamma processes, the false alarms would increase. Furthermore, this study derives the true upper and lower control limits when the X_bar control chart is used to monitor a gamma process. This study employs the Monte Carlo technique to determine the upper and lower control limits when the S control chart is used to monitor a gamma process. The fruitful results with the use of proposed approach are also demonstrated.

目 錄

摘要 I
目錄 III
圖目錄 IV
表目錄 V


第一章 緒論 1
第一節 研究背景 1
第二節 研究動機與目的 2
第三節 研究流程 4
第二章 文獻探討 6
第三章 問題論述與研究方法 10
第一節 問題闡述 10
第二節 方法論 14
第三節 參數估計式之統計性質 24
第四章 範例 34
第一節 模擬範例步驟 34
第二節 範例結果之比較 36
第五章 結論與未來研究方向 47
第一節 結論 47
第二節 未來研究方向 48
參考文獻 50
附錄A Fortran程式碼與註解 53
附錄B Gamma其餘參數組合之偏誤與均方誤 71
附錄C Gamma其餘參數組合S管制圖管制界限之蒙地卡羅估計值 77

圖目錄

圖1-1 研究流程圖 5
圖3-1 常態分配之模擬資料示意圖 11
圖3-2 Gamma分配之模擬資料示意圖 14
圖4-1 不同子群樣本下估計量之偏誤 (δ=1.1) 30
圖4-2 不同子群樣本下估計量之偏誤 (δ=1.5) 30
圖4-3 不同子群樣本下估計量之偏誤 (δ=2.0) 31
圖4-4 不同子群樣本下估計量之均方誤 (δ=1.1) 32
圖4-5 不同子群樣本下估計量之均方誤 (δ=1.5) 32
圖4-6 不同子群樣本下估計量之均方誤 (δ=2.0) 32
圖B-1 G（0.5,1）與不同δ，六種估計式偏誤與樣本數n之關係圖 71
圖B-2 G（2,1）與不同δ，六種估計式偏誤與樣本數n之關係圖 72
圖B-3 G（3,1）與不同δ，六種估計式偏誤與樣本數n之關係圖 72
圖B-4 G（4,1）與不同δ，六種估計式偏誤與樣本數n之關係圖 73
圖B-5 G（0.5,1）與不同δ，六種估計式均方誤與樣本數n之關係圖 74
圖B-6 G（2,1）與不同δ，六種估計式均方誤與樣本數n之關係圖 74
圖B-7 G（3,1）與不同δ，六種估計式均方誤與樣本數n之關係圖 75
圖B-8 G（4,1）與不同δ，六種估計式均方誤與樣本數n之關係圖 75

表目錄

表4-1 G（1,1） 之S管制圖管制界限之蒙地卡羅估計值 35
表4-2 10000次模擬實驗平均失控啟始時間與標準誤（n=2） 37
表4-3 10000次模擬實驗平均失控啟始時間與標準誤（n=3） 38
表4-4 10000次模擬實驗平均失控啟始時間與標準誤（n=4） 38
表4-5 10000次模擬實驗平均失控啟始時間與標準誤（n=5） 39
表4-6 10000次模擬實驗平均失控啟始時間與標準誤（n=10） 39
表4-7 10000次模擬實驗平均失控啟始時間與標準誤（n=15） 40
表4-8 10000次模擬實驗平均失控啟始時間與標準誤（n=20） 40
表4-9 10000次模擬實驗平均失控啟始時間與標準誤（n=25） 41
表4-10 10000次模擬實驗平均失控啟始時間與標準誤（n=30） 41
表C-1 G(0.5,1)之S管制圖管制界限之蒙地卡羅估計值 77
表C-2 G(2,1)之S管制圖管制界限之蒙地卡羅估計值 77
表C-3 G(3,1)之S管制圖管制界限之蒙地卡羅估計值 78
表C-4 G(4,1)之S管制圖管制界限之蒙地卡羅估計值 78

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