應用支援向量回歸建立剖面資料之監控方法

Application of Support Vector Regression in Profile Monitoring

吳薏苓(I-Lin Wu)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/碩士(2012年)

摘要

在統計品質管制 (SPC) 中常使用管制圖監控製程，隨著製程複雜性的增加，若繼續使用單變量管制圖進行監控將會造成嚴重之誤判。在許多管制之應用中，只利用一個或數個品質特性並不足以描述一個物件之品質，因此需要一個反應曲線或剖面來描述物件之品質，通常可以用線性回歸模型做為剖面提供描述模型。對於某些製程而言，品質特性之間可能是獨立的或是彼此之間具有相關性，但剖面 (profile) 製程之品質特性並非為單一分配之變數，而是一個函數。剖面是利用反應變數與一個或多個解釋變數間之關係所組成，而剖面製程之函數關係可呈現出線性、曲面以及離散等形式。然而在過去的研究中，對於剖面製程之監控仍採用管制圖進行監控。
為了提升線性剖面製程之績效，本研究提出建構支援向量回歸 (SVR) 之監控系統進行預測。在績效評估方面，本研究使用平均連串長度 (ARL) 做為績效指標，並以文獻中所提出之方法為比較基準。本研究提出三種不同之預測模型來監控線性剖面製程，並考慮四種不同偏移之型態 (截距、斜率、誤差項變異數以及截距與斜率同時發生偏移)，進而探討每一種型態在不同偏移程度下之監控績效。由研究結果顯示，以本研究所提出之三個 SVR 模型加入移動視窗概念之監控方法，在不同偏移程度下均能有效地提升偵測績效。

關鍵字

剖面製程 ； 線性剖面 ； 支援向量回歸 ； 平均連串長度

並列摘要

Statistical process control (SPC) has been successfully applied in a variety of areas. In some applications, it is usually assumed that quality characteristics can be adequately represented by one single measurement from an univariate or multivariate distribution of a vector formed by multiple measurements. However, in an increasing number of applications, there is an interest in monitoring multiple measurements constituting a line or curve. The quality of process control is characterized by the relationship between a response variable ( ) and one or more explanatory variables ( ), which is referred to as a profile. Thus, the profile monitoring process control detects and classifies the change occurred in a functional relationship of a process. The functional relationship of the profile can be presented by a linear, nonlinear or curve surface.
In this paper we use support vector regression (SVR) to detect and classify the shifts in linear profiles. Each of the three different prediction models based on support vector regression monitors the coefficients in a simple linear regression model of a profile, respectively. In performance evaluation, we use ARL criterion to assess the efficiencies of detecting shifts in linear profile data. After comparing with the traditional methods, the results of the proposed methods are better, which leads to enhancement in the monitoring performance. The main contribution of this research is enhancing the monitoring efficiency.

並列關鍵字

process profile ； linear profile ； support vector regression ； average run length

參考文獻

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Cheng, C. S., “A multi-layer neural network model for detecting changes in the process mean,” Computers & Industrial Engineering, 28, 1, 51-61 (1995).

Chinnam, R. B., “Support vector machines for recognizing shifts in correlated and other manufacturing processes,” International Journal of Production Research, 40, 4449-4466 (2002).

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