運用穩健之多變量管制圖於異常點偵測之研究

Robust Multivariate Control Chart for Outlier Detection

黃惠國(Hui-Kuo Huang)

指導教授 ： 范書愷

元智大學/工程學院/工業工程與管理學系/碩士(2011年)

https://doi.org/10.6838/YZU.2011.00114

摘要

本研究之目的是設計兩個全新的多變量管制圖(multivariate control chart)以有效偵測(detection)多維度資料中潛在的異常點 (outlier)，使得掩蔽效應(masking effect)及淹沒效應(swamping effect)均在控制之內。文中利用預測平方誤差(predicted squared error)以及階層式分類樹(hierarchical cluster tree)分別來改善Sullivan 和Woodall於1996年所提出的第二個方法(Sullivan and Woodall second approach, SW2)。利用多維度的歷史數據(multivariate historical dataset)來分析各方法之綜合表現，再以模擬研究(simulation study) 透過蒙地卡羅實驗(Monte Carlo experiments)驗證本研究所提出之管制方法較文獻中現有之方法更能夠穩健及更快速(較MVE快約數十倍至一百倍)的提供正確的異常點偵測。

關鍵字

異常點 ； 多變量管制圖 ； 掩蔽效應 ； 淹沒效應 ； 預測平方誤差 ； 階層式分類樹

並列摘要

The aim of this thesis is to design two new multivariate control charts that can effectively detect potential outlier(s) in multi-dimensional data while keeping the masking and swamping effects under control. Predicted squared error and hierarchical cluster tree are augmented into the proposed control charts, respectively, to improve the Sullivan and Woodall second approach (SW2). Multivariate historical datasets are borrowed to illustrate the performance comparisons between various methods. A simulation study based on Monte Carlo experiments further verifies that the proposed method is more robust and 60-100 times faster than MVE in computation time for outlier detection than existing methods in the literature.

並列關鍵字

swamping effect ； predicted squared error ； hierarchical cluster tree ； outlier ； multivariate control chart ； masking effect

參考文獻

Allen, D. M. (1971), “Mean Square Error of Prediction as a Criterion for Selecting Variables,” Technometrics, 13, 469-475.

Allen, D. M. (1974), “The Relationship between Variable Selection and Data Augmentation and a Method for Prediction,” Technometrics, 16, 125-127.

Atkinson, A. C., and Mulira, H. M. (1993), “The Stalactite Plot for the Detection of Multivariate Outliers,” Statistics and Computing, 3, 27-35.

Barnett, V., and Lewis, T. (1984), Outliers in Statistical Data, 2nd Edition, John Wiley & Sons, New York.

Brownlee, K. A. (1965), Statistical Theory and Methodology in Science and Engineering, 2nd Edition, John Wiley & Sons, New York.