臺灣博碩士論文加值系統

管制圖的平均連串長度（Average run length，ARL）是管制圖對異常製程的偵測能力指標。管制圖的平均連串長度有兩種：當製程正常，管制圖判為異常的平均抽樣次數稱為平均連串長度ARL0；製程異常，管制圖判為異常的平均抽樣次數稱為連串長度ARL1。好的管制圖是ARL0 愈大，ARL1 愈小。本論文的目的就是找出ARL0 最大與ARL1 最小的P管制圖參數。
首先使用中央合成設計配置影響P管制圖平均連串長度之因子：樣本數、抽樣間隔、管制界限係數、製程異常率、製程異常偏移量。經由電腦模擬中央合成設計的47種處裡組合，得ARL0與ARL1，再配適ARL0與ARL1的二階反應曲面模式，最後利用偏微分極大化ARL0與ARL1之差，獲得P管制圖的最佳參數。
關鍵

The average run length is an index to present the ability of process-diagnosis by the control chart. Under the normal process, the average number of sampling, used to identify that the process is out-of-control in the control chart, is called the average run length ARL0. Under the abnormal process, the average number of sampling, used to identify that the process is out-of-control in the control chart, is called the average run length ARL1. The ARL0 of the control chart is the larger the better and ARL1 is the smaller the better. The purpose of this paper is to look for the parameters of the P control chart that make the ARL0 largest and the ARL1 smallest.
The parameters of the P control chart that affect the average run length are sample size, sampling intervals, control limit coefficient, out-of-control probability and shift amount of defective proportion. These parameters are arranged by central composite design which includes 47 treatment combinations. Computer simulation each treatment combination, we get 47 pairs of ARL0 and ARL1 which use to fit the second-order response surface model of ARL0 and ARL1. And finally, maximize the difference between the ARL0 and ARL1 use partial differential to get the best parameter combination of the P control chart.

目錄
誌謝 i
摘要 ii
Abstract iii
圖目錄 vi
表目錄 vii
第一章 緒論 1
1.1 研究動機與目的 1
1.2 研究假設 2
1.3 論文架構 3
第二章 文獻探討 5
2.1 SHEWHART P管制圖 5
2.3 平均連串長度 10
第三章 研究方法 14
3.1 中央合成設計 15
3.2 電腦模擬 19
3.2.1 MATLAB 19
3.2.2 電腦模擬過程 21
3.3 反應曲面及其最佳化 25
第四章 模擬數據分析 28
4.1 ARL0與ARL1反應值 28
4.2 數據分析 31
4.2.1 ARL0變異數分析 31
4.2.2 ARL1變異數分析 34
4.3 P管制圖參數最佳化 37
第五章 結論與建議 40
5.1 結論與建議 40
5.2 未來研究方向 40
參考文獻 41
附錄 MATLAB模擬程式碼 43

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