應用k最近鄰資料描述法建立多變量管制圖：以監控印刷電路板雷射鑽孔製程為例

THE APPLICATION OF k NEAREST NEIGHBORS DATA DESCRIPTION FOR MULTIVARIATE PROCESS MONITORING: A CASE STUDY OF PRINTED CIRCUIT BOARD LASER DRILLING PROCESS

何應(Ying Ho) ； 鄭春生(Chuen-Sheng Cheng) ； 謝定緁(Ting-Chien Hsien)

《品質學報》 25卷6期 (2018/12) Pp. 399-413

https://doi.org/10.6220/joq.201812_25(6).0003

摘要

本研究以單類別k最近鄰資料描述(k nearest neighbors data description, kNNDD)演算法為基礎，發展一個多變量製程管制方法。此管制方法只利用管制內資料來建立，同時不需要任何有關資料分配的假設。本研究利用kNNDD演算法所獲得的新穎分數作為管制統計量，發展一個稱為kNN之管制圖。本研究將針對重要的參數，提出有系統性的決定方式。另外，本研究也提出一個新的方法，將單類別資料轉換成管制內和管制外之二元類別資料，並以支援向量迴歸(support vector regression, SVR)建立監控程序。本研究以平均連串長度(average run length, ARL)作為績效評估指標，透過模擬之方式評估kNN管制圖和T2管制圖，在不同偏移情況下之偵測績效。研究結果顯示，本研究所提出之方法可以有效地偵測製程之異常偏移。另外，SVR也可以進一步提升偵測績效。本研究也以印刷電路板之鑽孔製程為例，收集多變量製程資料，驗證本研究所提出kNN管制圖在實務上應用之可行性。

關鍵字

k最近鄰資料描述演算法 ； 支援向量迴歸 ； 平均連串長度 ； 多變量製程管制

並列摘要

In this research, we propose a multivariate process control method by integrating the k nearest neighbors data description (kNNDD) algorithm and support vector regression (SVR). The proposed method does not require any distributional assumptions. The research considers the situation that there is an in-control dataset only in the chart building. The monitoring statistics of the proposed method are obtained from the novelty scores of the kNNDD algorithm. We propose two control chart designs for multivariate process. In the first design, a one-class kNNDD-based control chart is proposed. This research addresses the issues on determining the important parameters. In the second design, a one-class classification-based control chart is converted to a prediction problem based on SVR algorithm. A procedure to build the two-class training dataset for SVR is proposed. With optimized kNNDD procedure, some observations that are obviously different from in-control observations are labeled as out-of-control class. With two classes of observations, an SVR-based control procedure can be developed. An extensive simulation study was conducted to examine the properties of the proposed control chart under various scenarios and compare it with existing multivariate control charts in terms of average run length (ARL) criterion. The results indicate that the proposed method performs better than traditional control chart. The applicability of the proposed approach is also demonstrated with real data collected from printed circuit board (PCB) laser drilling process.

並列關鍵字

k nearest neighbors data description ； support vector regression ； average run length ； multivariate process control

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