藉由近似線性的分段監控非線性剖面

許多實際製程情況下，使用一個或多個解釋（可控）變數與反應變數之間的關係來描述製程或產品之品質特性是比較適當的。在許多情况下，反應變數Y和解釋變數X之間的關係可以由剖面（profile）來呈現。近幾年來，監控剖面資料在統計製程監控領域已經成為熱門研究議題。但實際上，文獻中對於非線性剖面製程監控並無太多著墨。本研究將非線性剖面分割成近似線性的多重線段，並且分別監控每一個分段；也就是說，在Phase I的監控包含了建立模型並估計管制界線，而在Phase II監控時，利用所估計出的管制界線來監控製程。本研究提出了新的方法來決定剖面上的變化點數量及其位置，以便分割非線性剖面，並利用兩個準則來決定最佳變化點數量以避免過度配適情況發生，同時使用多個製程剖面資料來測試本研究提出的方法以說明其可行性。文中也使用平均串聯長度（average run length）來比較多變量管制圖及EWMA3這兩種監控方法之優劣。本論文最後使用垂直密度剖面資料（vertical density profiles）為例，使用多變量管制圖配合線性近似分段來達到非線性剖面資料監控的目的，在模擬實驗中分別改變不同模型參數，以模擬製程處於非管制狀態下，比較本研究方法與Williams et al. （2007）製程監控績效。

關鍵字

非線性剖面；變化點；統計製程監控；垂直密度剖面資料；赤池資訊準則； Schwarz資訊準則

並列摘要

In many practical situations, the quality of a process or product is better characterized and summarized by the relationship between a response variable and one or more explanatory variable(s). In many cases, there is a relationship between the response variable Y and explanatory variables X that can be represented by a profile. In recent years, profile monitoring has been a popular and fertile field of research in statistical process control. In fact, little work has been done to address the monitoring of nonlinear profiles. In order to monitor the whole nonlinear profiles, this thesis focuses on segmenting the entire nonlinear profile into several linear approximations and monitoring each segment separately. That is to say, included in Phase I analysis are model building and the parameter estimation required to construct the control limits. In Phase II, the control limits are used to monitor the process. Here, this thesis proposes a new method for determining the number and the location of change points. Two criterions are used to select the best number of change points to avoid over fitting. Some manufacturing profiles are presented to verify the proposed method. The ARL comparison between method and EWMA3 (2003) are demonstrated based on the premise that the nonlinear profile is fitted by the proposed change point model. Lastly, the vertical density profile data is used to evaluate the monitoring performance between the proposed method and Williams et al. (2007).

並列關鍵字

Nonlinear Profile ； Change Points ； Statistical Process Control (SPC) ； Vertical Density Profiles (VDP) ； Akaike’s Information Criterion (AIC) ； Schwarz Information Criterion (SIC)

參考文獻

Akaike, H. (1974), “A new look at the statistical model identification,” IEEE Transactions on Automatic Control, 19(6), 716-723.

Ding, Y., Zeng, L. and Zhou, S. (2006), “Phase I Analysis for Monitoring Nonlinear Profiles in Manufacturing Processes,” Journal of Quality Technology, 38(3), 199-216.

Doty, L.A. (1996), Statistical Process Control, Second Edition, Industrial Press Inc., New York, 1-42.

Hawkins, D.M. (1976), “Point Estimation of the Parameters of Piecewise Regression Models” Applied Statistics, 25(1), 51-57.

Hawkins, D.M. (2001), “Fitting Multiple Change-Point Models to Data” Computational Statistics & Data Analysis, 37, 323-341.

國際替代計量

藉由近似線性的分段監控非線性剖面

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