利用非相關成份分析執行統計製程監控

Statistical Process Monitoring with Uncorrelated Component Analysis

王議億(Yi-Yi Wang)

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(2007年)

摘要

利用非相關成份分析(uncorrelated component analysis)來解決混合的製程訊號，並且結合質群演算法(particle swarm optimization)來達到最佳化的目的。在混合的製程訊號分離效果中，利用非相關成份分析可以有效的分離自我相關序列(autoregressive series)、製程平均值偏移，以及白色噪音(Gaussian noises)的混合製程訊號。此外在製程監控上，配合指數加權移動平均管制圖(EWMA control chart)可以有效的降低偵測平均值偏移的平均連串長度(average run length)。

關鍵字

製程監控 ； 獨立成份分析 ； 非相關成份分析 ； 質群演算法

並列摘要

The uncorrelated component analysis (UCA) model is applied to solving the mixed process signal separation problem. In order to seek optimum demixing matrix of UCA model, particle swarm optimization (PSO) which is one of the latest developed population-based optimization methods is adopted. In the context of signal separation, the presented method could find efficiently and reliably the optimal estimate of the demixing matrix for the mixed process signals, such as autoregressive (AR) series, step change in process mean, and Gaussian noises. Furthermore, the proposed method can be applied to EWMA control chart in process monitoring to detect small shift in process mean with shorter out-of-control average run length (ARL).

並列關鍵字

Process monitoring ； Independent component analysis (ICA) ； Uncorrelated component analysis (UCA) ； Particle swarm optimization (PSO)

參考文獻

Chatterjee, A., and Siarry, P., "Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization," Computers and Operations Research, Vol. 33, No. 3, 2006, pp. 859-871.

Comon, P., "Independent component analysis. A new concept?" Signal Processing, Vol. 36, No. 3, 1994, pp. 287-314.

Courant, R., "Variational methods for the solution of problems of equilibrium and vibrations," Bulletin of the American Mathematical Society, Vol. 49, 1943, pp. 1-23.

Cover, T.M., and Thomas, J.A., "Elements of Information Theory," Wiley, New York, 1991.

del Castillo, E., "Statistical Process Adjustment for Quality Control," Wiley, New York, 2002.