利用Oja 資料縱深測度建構剖面資料之無母數監控方法

對於品質特性可以藉由剖面資料加以描述的製程，基於資料縱深測度，我們提出一些無母數製程監控方法。我們首先回顧剖面資料監控、數據平滑化、主成分分析、階層式集群方法與資料縱深測度管制圖等文獻。在此我們聚焦於階段二的非線性剖面資料監控。對於所提出的製程監控方法，其最大優點在於不需要對剖面資料做有母數形式之分配假設。我們根據平均連串長度，透過模擬的方式與現存藉由無母數迴歸且在高斯分配假設下所發展出來的監控方法做比較。對於階段一的分析，我們提出一個具啟發性的診斷程序藉此去除潛在失控的剖面資料。在此透過一組生物鑑定實驗資料與一組垂直密度剖面資料 (VDP)來展示我們所提出的診斷程序。

關鍵字

剖面；數據平滑化；主成分分析；階層式集群方法；資料縱深測度；平均連串長度

並列摘要

We propose and study some nonparametric process monitoring schemes based on data depth for processes where the quality of a product could be characterized by a function or a profile. We start by reviewing some literatures on profile monitoring, data smoothing, principal component analysis, hierarchical clustering methods, and data-depth-based control charts. We focus on Phase II profile monitoring for nonlinear profiles with random effects. The great advantage of the proposed monitoring schemes is that neither a parametric form nor distributional assumptions about the profiles are required. We compare the proposed schemes with some existing schemes developed via nonparametric regression but under Gaussian assumption in terms of the average run length by simulation. For Phase I analysis, we provide a heuristic diagnosis procedure for screening out potential out-of-control profiles. The bioassay data and vertical density profile (VDP) data are used to demonstrate the diagnostic scheme.

並列關鍵字

profile ； data smoothing ； principal component analysis ； hierarchical clustering ； data depth ； average run length

參考文獻

[1] Johnson, R. A. and Wichern, D. W. (2007). Applied Multivariate Statistical Analysis.

[2] Kang, L. and Albin, S. L. (2000). On-Line Monitoring When the Process Yields a

[3] Kim, K., Mahmoud, M. A., and Woodall, W. H. (2003). On The Monitoring of

[4] Liu, R. Y. (1990). On a Notion of Data Depth Based on Random Simplices". The

Annals of Statistics. 18, 405-414.

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利用Oja 資料縱深測度建構剖面資料之無母數監控方法

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