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    政大機構典藏 > 商學院 > 統計學系 > 期刊論文 >  Item 140.119/66645


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/66645


    Title: X-S[feb4]區域管制圖的最適設計
    Other Titles: The Optimal Design of X-S[feb4] Zone Control Charts
    Authors: 楊素芬;陳智鴻
    Yang, Su-fen;Chen, S.
    Contributors: 統計所
    Keywords: 管制圖;馬可夫鏈;特殊原因;更新理論
    Control charts;Markov chain;Assignable cause;Renewal theory
    Date: 1996.03
    Issue Date: 2014-06-10 17:56:47 (UTC+8)
    Abstract: 自Duncan在1956年提出管制圖的經濟設計後，陸續有許多學者提出各種不同形態管 制圖經濟設計之研究。唯這些文章中，尚無將管制圖中描點 (plotted points) 的連串檢定 (run tests) 列入考慮。然而在管制圖中加入描點的某些連串檢定實有其必要，因加入連串 檢定後可增加管制圖的偵測能力。 但管制圖中加連串檢定不僅麻煩， 且亦會使錯誤警訊 (false alarm) 發生的頻率增加。 Jaehn(1987a) 提出區域管制圖的觀念以取代傳統管制圖 加上連串法則的不便。 本研究提出 X-S 區域管制圖的經濟設計以改善一般經濟管制圖未將 連串檢定列入考量的缺點。 另外我們應用 Saniga(1989) 經濟統計管制圖的觀念，設計經濟統計區域管制 圖，即在限制統計層面的要求下，計算得成本最小下的最適設計參數值。一些數值分析結果 ， 將用以說明經濟設計與經濟統計設計下最適設計參數值、最適成本、型 I 誤差機率和檢 定力之差異。雖然經濟統計區域管制圖所計算得的成本會比以經濟區域管制圖的成本稍大，但在統計表現方面卻符合我們所設定的基本要求。
    Shewhart(1931) originated control charts in the 1920s. Since then, much work has been done to improve the sensitivity of control charts to detect changes in process parameters. Jaehn(1987a) proposed the zone control chart as a further development in the area of simplifying, yet sensitizing, control charts. So far, the sensitivity of economic control charts to detect changes in process parameters has not been addressed. In this paper we consider the economic design of X-S[feb4] zone control charts when there is a single assignable cause which affects the process mean and increases the process variation. In addition, we propose a statistically constrained economic design of X-S[feb4] zone control charts to maintain the effectiveness of economic design and reduce the frequency of false alarm as well as some possible incorrect adjustments. The differences between economic design and statistically constrained economic design are illustrated numerically in terms of optimum design parameters, optimum costs, type I error probabillities, and powers. We find that the increased cost was relatively small, and the frequency of false alarms and the time to detect the assignable cause are significantly reduced in the statistically constrained economic design of X-S[feb4] zone control charts.
    Relation: 中國統計學報, 35(1), 63-80
    Data Type: article
    Appears in Collections:[統計學系] 期刊論文

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