輪廓製程為現代工業中很常見的製程之一，其中輪廓為一種由一個或多個解釋變數與反應變數之間的函數關係來描述產品品質的方法。在現行的文獻中，對於監控線性輪廓製程的管制圖大多數都有在輪廓模型中對誤差項做常態分配的假設。本文主要探討的議題則是在輪廓模型中誤差項沒有常態分配的假設下，針對第二階段線上的線性輪廓製程做監控。我們利用對數線性模型與皮爾森卡方檢定來建立管制統計量，得到一個無母數的CUSUM管制圖，並且用統計模擬的方式討論我們所提的管制圖在監控上效率的表現，最後舉一個實例來說明如何在實務上運用我們所提的管制圖。

Profile process is a common process in the modern industry manufacturing. Profile is a method used to describe quality of product by relationship between one or more explanatory variables and reaction variable. In current literature, there is a normal distribution assumption of the error terms in majority control chart for monitoring linear profiles. In this article we focus on the assumption that he error term do not have normal distribution, do on-line monitoring on phase II linear profiles. We used log-linear model and Pearson chi square test to construct charting statistics. Then used these statistics establish a nonparametric CUSUM control chart. Thus we used statistic simulation to investigate the efficient performance about the control chart we proposed. At last, we used an example to illustrate the control chart we proposed.

目錄
第一章緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 輪廓監控. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
第二章監控線性輪廓. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 利用對數線性模型估計管制狀態下的分配. . . . . . . . . . . . . . 6
2.2 建構CUSUM 管制圖來監控線性輪廓製程. . . . . . . . . . . . . . 9
2.2.1 線性輪廓模型與參數估計. . . . . . . . . . . . . . . . . . . 9
2.2.2 監控第二階段的線性輪廓製程. . . . . . . . . . . . . . . . . 11
第三章統計模擬. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.1 管制圖效率的比較. . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 第一階段資料個數的影響. . . . . . . . . . . . . . . . . . . . . . . 22
3.3 實例. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
第四章結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
附錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
附表. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
附圖. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

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