整合平滑樣條法與決策樹於非線性剖面製程之研究

The Monitoring of Nonlinear Profiles Using Smoothing Spline and Decision Tree Model

10.6220/joq.2015.22(2).01

李虹葶(Hung-Ting Lee)；黃照雅(Jau-Ya Huang)；鄭春生(Chuen-Sheng Cheng)

非線性剖面 ； 無母數迴歸 ； 平滑樣條法 ； 決策樹 ； nonlinear profile ； non-parametric regression ； distance-based metrics ； decision tree

品質學報

22卷2期（2015 / 04 / 30）

77 - 87

繁體中文

在傳統統計製程管制（statistical process control, SPC）之應用中，我們假設一個物件或製程之品質，可以由一個量測值或來自多變量分配之數個量測值來描述。但在許多實務應用中，我們需要監控一條由數個資料所構成之直線或曲線。這些直線或曲線被稱為剖面（profile）或函數。剖面資料可以利用一個線性或非線性之模型來表示。本研究之目的是建立監控非線性剖面製程之管制程序。此管制程序包含利用屬於無母數迴歸之平滑樣條法來建立參考剖面，接著再發展出以距離為基之特徵值。一個決策樹分類模型利用這些特徵值來進行剖面製程之監控。本研究所提出之管制程序是以彩色濾光片的銦鋅氧化物製程資料，來驗證其可行性和有效性。研究結果顯示，使用平滑樣條法可以有效地去除雜訊，其建立的平滑曲線可以作為參考剖面。深入的比較顯示，本研究所提出的特徵值，可以有效地提升決策樹之分類正確率，進而提升監控非線性剖面之效益。

In traditional statistical process control (SPC) applications, it is assumed that the quality of a product or process can be characterized by a single measurement from a univariate distribution or multiple measurements from a multivariate distribution. However, in some practical applications, there is a demand in monitoring multiple measurements constituting a line or curve that is often referred to as a profile or function. Such profiles can be represented by a linear or nonlinear model. This paper focuses on the monitoring of nonlinear profiles. We propose using non-parametric regression method to construct a reference (baseline) profile. A set of relevant statistics based on distance-based metrics is used to construct a feature vector for a decision tree-based monitoring procedure. The implementation of the proposed approach is illustrated using the profile data obtained from industry. A comparative study shows that the proposed method is capable of detecting the changes in a profile.

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