應用獨立成分分析與蕭華特管制圖於統計製程監控

Statistical Process Monitoring Using Independent Component Analysis and Shewhart Control Chart

統計製程管制（Statistical Process Control, SPC）為品質管制中最重要的技術之一，其目的是在製程中尋找造成品質變異的來源，以降低產品之間的差異，並提高產品水準與製程能力。管制圖（control charts）是SPC中最常用的工具之一，其主要的功能在於協助製程人員尋找並去除干擾製程的可歸屬原因（assignable causes），以達成改善製程及維持產品品質之目的。傳統的管制圖假設製程觀察值在不同的時間下為具有相同分配且彼此獨立的隨機變數，但實際的製程常是相關性製程，製程的觀測值會存在自我相關。若將相關性製程的資料直接以傳統管制圖進行監控往往無法得到良好的監控結果，而需要對資料進行繁複的處理以獲得較容易進行監控的資料。由於相關性製程資料可被視為一個混合了雜訊及製程干擾項的混合資料（mixture data），因此本研究導入近年來快速發展用於訊號分離（signal separation）之獨立成分分析（Independent Component Analysis, ICA）技術於統計製程管制中，利用ICA能將混合訊號分離出潛在來源訊號（latent source signals）之能力，提出一個結合獨立成分分析與蕭華特管制圖（Shewhart control chart）之製程監控架構。所提架構為將製程觀察值（即混合訊號）先利用ICA分離出包含不同品質特性之獨立成分（independent component），接者再以傳統的蕭華特管制圖對獨立成分進行監控，期望能解決傳統蕭華特管制圖需要對相關性製程的資料進行繁複處理的問題。本研究利用具時間序列模式AR（1）及ARMA（1, 1）的模擬製程資料來比較所提方法與傳統蕭華特管制圖、SCC管制圖、EWMA管制圖、EWMAST管制圖及ARMAST管制圖之監控能力。實驗結果顯示，本研究所提之方法在製程具自我相關時，有較上述管制圖為佳的監控結果

Statistical process control (SPC) has been used extensively to monitor and improve the quality of process. The traditional SPC control charts assume that process data are identically and independently distributed. However, the real process data are actually serially correlated. The presence of autocorrelation has an adverse effect on the performance of traditional SPC control charts. To alleviate this problem, one of the popular approaches is to use time series model to fit the data, then apply the traditional control charts to the residuals. The major limitation of the time series based approaches is that time series modeling of the process data is not always straightforward. Since the correlated process data could be a mixture of noise and process characteristics such as process disturbances and/or autocorrelation, a process monitoring scheme based on independent component analysis (ICA) is proposed for correlated process. ICA is a novel statistical signal processing technique that was originally proposed to find the latent source signals from observed mixture signal, without knowing any prior knowledge of the mixing mechanisms. The proposed scheme first applies ICA methodology to the process observations to generate the independent components that contain different characteristics of the process. The traditional Shewhart control chart is then used to monitor the independent components for process control. The experimental results reveal that the proposed method outperforms Shewhart, SCC, EWMA, EWMAST and ARMA control charts in most instances and is effective for monitoring correlated process.