使用代理變數下的監控過程及適應性管制圖設計
學年 97
學期 1
出版（發表）日期 2009-01-01
作品名稱 使用代理變數下的監控過程及適應性管制圖設計
作品名稱（其他語言） Designs of Screening Procedure and Adaptive Control Chart with Surrogate Variables
著者 蔡宗儒
單位 淡江大學統計學系
描述 計畫編號：NSC98-2118-M032-008 研究期間：200908~201007 研究經費：492,000
委託單位 行政院國家科學委員會
摘要 在很多情況下直接對有興趣的品質特徵做監控需要較高的成 本， 但透過對與其相關的代理變數做監控時則可減少成本的支出， 並提高利潤。本計畫主要分成兩個部分來探討如何使用代理變數建 立最佳的監控程序及建立適應性管制圖。其執行順序如下: 第一部分：將針對使用與產品品質相關的代理變數建立滿足期望利 潤極大化之最佳的製程平均及監控管制界限。此利潤函數考慮 了包括銷售成本、生產成本、再製成本、檢查成本和處罰成本。 本計畫修正了Le e e t a l . ( 2 0 0 0 ) 的程序， 並從另外一個更合 理觀點來看我們推廣的利潤函數和L ee et al. (2000)所提出 的利潤函數的關係，以發展最佳的監控程序，研究中並將執行 一個數值研究，以評估此方法的績效。 第二部分：在節省成本的考量下，討論交錯使用代理變數及感興趣 的品質特徵變數，並利用馬可夫鏈方法建立一個兩階段的適應 性管制圖。當第一個階段中以代理變數所建立的管制圖有錯誤 預警時， 監控程序才轉到以績效變數建立的管制圖繼續監控， 然後再依績效變數之觀察狀態決定是否回到以代理變數做監 控的管制圖或發生失控的預警訊號。詳細的管制流程及最佳的 參數解將在本研究中被討論。一個數值研究會被執行，以評估此方 法的績效。 The cost of measuring the quality characteristic of interest on performance variable is often too high in real world applications, a surrogate variable which is correlated with the performance variable and less expensive to measure can be considered for developing the optimum screening procedure and control charts. The project is then motivated to develop the optimum screening procedure and a two-stage adaptive control chart by employing surrogate variables as follows: Part I: Considering the problem of determining the optimum process mean and screening limits with a surrogate variable. Assume that the performance and surrogate variables are jointly normally distributed. The optimum process mean and screening limits are determined by maximizing the expected profit function which includes selling price, production, reprocessing, inspection and penalty cost. The research modifies the viewpoint of Lee et al. (2000) and develops the optimum screening procedure based on a more reasonable generalized profit function. The connection of the generalized profit function and the profit function of Lee et al. (2000) will be addressed in this research. A numerical study is conducted to evaluate the performance of the proposed method. Part II: A two-stage adaptive control chart with variable sampling interval is developed for monitoring the process mean when a surrogate variable is employed. The suggested procedure starts to monitor the process based on the surrogate variable until it signals an out-of-control, and then the monitoring switches to the control chart which is developed by the performance variable. The control chart limits are determined based on the Markov chain approach, and the detail switching steps between two control charts are constructed. A numerical study is conducted to evaluate the performance of the proposed method.
關鍵字 績效變數; 監控界限; 監控程序; 代理變數; 兩階段的管制圖; Performance variable; screening limits; screening procedure; surrogate variable; two-stage control chart
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