在許多工業製造的例子上，產品或製程的品質可以用一個反應變數以及一個或多個解釋變數的函數關係來描述，這種函數關係稱為輪廓製程，而管制圖是統計製程管制(statistical process control，簡稱SPC) 中最為廣泛使用的監控輪廓製程的方法。在本篇論文中，我們探討使用Zou, Tsung and Wang (2007) 的MEWMA (multivariate EWMA) 管制圖來監控一般線性輪廓製程優劣點，並對於實用上的缺點提出補助之道。首先，我們比較此管制圖和其它用來監控線性輪廓製程管制圖的表現，接著我們想要了解需要使用多少組第一階段的管制狀態資料才能使真實的(true) 管制狀態平均連串長度(ARL0) 達到名義的(nominal)ARL0。在一般情形下，通常沒有辦法蒐集到大量的第一階段資料，所以我們藉由拔靴法來調整管制界限，保證在調整後的管制界限之下，有一固定的機率使得真實的ARL0 大於名義的ARL0。最後，我們會用一個實際的例子來說明如何使用調整管制界限與非調整管制界限來監控線性輪廓製程。

In many industrial manufacturing processes, the quality of a process or product is represented by a relationship between the response variable and one or more explanatory variables. We call this relationship profile process. Control chart is the most widely used to monitor profile process in the statistical process control (SPC). In this article, we are going to investigate strengths and weakness of Zou, Tsung and Wang (2007) MEWMA chart which is used to monitor general linear profiles. Then provide a method to solve the practical shortcomings. First, we compare the performances between this chart and other charts which are used to monitor linear profiles. Then we want to know how many in-control phase I datasets can make true in-control average run length (ARL0) achieve nominal ARL0. In general case, usually can’t collected a lot of phase I datasets. So we adjust control limit by bootstrap, which can guarantee that use the adjusted control
limit have a fixed probability let true ARL0 more than nominal ARL0. At the end, a real example is used to illustrate how to use adjusted and unadjusted control limit for monitoring linear profiles.

目錄
第一章 續論1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 管制圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 輪廓製程監控. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
第二章 第一階段資料對第二階段線上監控的影響7
2.1 線性輪廓製程監控的模型. . . . . . . . . . . . . . . . . . . . . . 7
2.2 不同管制圖監控簡單線性輪廓製程的表現. . . . . . . . . . . . . 10
2.2.1 非管制狀態下的表現. . . . . . . . . . . . . . . . . . . . . 11
2.2.2 管制狀態下的表現. . . . . . . . . . . . . . . . . . . . . . 14
2.3 第一階段資料的大小選擇. . . . . . . . . . . . . . . . . . . . . . 17
第三章 保證管制圖18
3.1 利用拔靴法調整管制界限. . . . . . . . . . . . . . . . . . . . . . 18
3.2 調整管制界限的表現. . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 實例分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
第四章結論27
附錄28
參考文獻32
附表36
附圖58

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