利用對數線性模型來監控線性輪廓製程的無母數管制圖

A Nonparametric Control Chart to Monitor Linear Profiles Based on Log-Linear Model

廖彥銘(Liao, Yen Ming)

指導教授 ： 黃榮臣

國立清華大學/理學院/統計學研究所/碩士(2016年)

摘要

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。

關鍵字

管制圖 ； 輪廓監控 ； 對數線性模型 ； 無母數

並列摘要

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.

參考文獻

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Control Charts via Bootstrap Methods”. Scandinavian Journal of Statistics