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題 名 | X-管制圖條件管制界限之建構與分析--以AR(1)相關性資料為例=Analysis of Conditional Control Limits of X-Control Chart for AR(1) Correlated Data |
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作 者 | 陳雲岫; | 書刊名 | 中國統計學報 |
卷 期 | 35:4 1997.12[民86.12] |
頁 次 | 頁379-398 |
分類號 | 494.56 |
關鍵詞 | X-管制圖; 條件管制界限法; 相關性; 平均連串長度; 傳統管制界限法; 蒙地卡羅模擬; Average run length; Conditional control limits; Conventional control limits; Correlation; Monte carlo simulation; X-control chart; |
語 文 | 中文(Chinese) |
中文摘要 | 本文針對AR(1)型態資料,提出以前一期之資料,建構 X--管制圖之管制界限, 作為下一期資料之判定準則之條件管制界限法。在參數值已知下,分別推導連串長度在條件 管制界限法與傳統管制界限法下之分配,期望值及變異數。以平均連串長度為評估指標來比 較兩種管制界限法在 AR(1) 模式下之差異,並利用模擬方法分析平均連串長度, 及其變異 數與參數間之關係。分析結果顯示在對立假設下,傳統管制界限法之平均連串長度和變異數 ,均會隨著相關係數的絕對值增加而增加,且當比較絕對值一樣但正負相反的兩個相關係數 時,負相關係數的平均連串長度值及變異數比正相關係數者小。在相關係數固定下,兩種管 制界限法之連串長度平均值與標準差會隨著平移幅度遞增而遞降,與平移方向無關。若是製 程在控制 (虛無假設 ) 下,則傳統管制界限法表現優於條件管制界限法。 且相關係數之絕 對值越大則前者之平均連串長度值越大,然條件管制界限法的連串長度平均值及變異數則不 受相關係數影響,為一常數。反之,若製程發生變化,則條件管制方法能較快偵測出異常現 象,其敏感度優於傳統之管制界限法。 |
英文摘要 | In this research, we construct conditional control limits of X--control chart for AR(1)correlated data. The spirit of the conditional control limits is to construct a new pair of limits based on the previous observation at each stage. The average run length is used as an evaluation index and both distributions of run lengths for the conditional and the conventional control methods are derived. Numerical comparsions for both methods under various parameter combinations are performed by Monte Carlo simulations. The simulation results show that both the mean and the variance of run length for the conventional method increase as the absolute value of correlation coefficient increases. Also, in the case of fixed correlation coefficient, those for both control methods decrease as the shift amount increases, and are independent of the direction of the shift. If the process is under the control, then the conventional method is superior to the conditional method. However, if the process is out of control, then the conditional method is better than the conventional one. |
本系統中英文摘要資訊取自各篇刊載內容。