應用主成分分析與MEWMA管制圖監控多變量管制圖之非隨機樣式

Pattern Recognition of Multivariate Process Using Principal Components Analysis and MEWMA Control Chart

張沛琳(Ping-Chen Chang)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/碩士(2008年)

摘要

由於科技之進步，先進的自動化檢測設備能同時量測一件產品中多項品質特性，若同時以多個單變量管制程序監控此多個品質特性，可能無法偵測出製程異常之因素，所以當製程具有多個相關之品質特性時，即為本研究所探討之多變量品質管制問題，通常都是以多變量管制法處理此類問題。多變量管制法主要在偵測多變量製程異常之發生，進而發展出有效之監控系統，可及早偵測製程之變化。若製程存在可歸屬原因，則管制圖上之樣本統計量會超出管制界限或呈現特定之非隨機樣式。管制圖中常見之非隨機樣式包括：趨勢樣式、偏移樣式、混合樣式與週期性樣式等。

在多變量管制圖中，包含了許多監控製程平均數的管制圖，如 Hotelling 管制圖、多變量累積和 (multivariate cumulative sum, MCUSUM) 管制圖、多變量指數加權移動平均 (multivariate exponentially weight moving average, MEWMA) 等管制圖。由於 管制圖對於製程中的微量變化不是很敏感，故本研究擬使用 MEWMA管制圖來監控製程中之非隨機樣式，並且利用主成份分析法 (principal component analysis, PCA) 降低變量的個數 MEWMA 管制圖的使用更為簡便。

關鍵字

非隨機樣式、多變量製程管制、MEWMA管制圖、主成份分析法

並列摘要

Because of the advancement of technology, the advanced automatic equipments can measure multiple quality characteristics of a product simultaneously. It is hard to find the unusual situation by using several univariate control chart in multivariate processes. It usually uses multivariate control chart to monitor the multiple relative quality characteristics. The purpose of the multivariate control charts is to detect the occurrence of some assignable cause which leads to the variations of multivariate processes, then an effective monitoring system is developed which can detect the variation of a process as soon as possible. If the variation occurred, the statistics in the control chart may exceed the control limits or exhibit in some specific non-random pattern, such as the trend pattern, cyclic pattern, sudden shift pattern and concurrent pattern.

There are many multivariate control chart such us Hotelling control chart, MCUSUM control chart and MEWMA control chart. Because of the insensibility in detecting the slight variations of the control chart, the MEWMA control chart and the principle component analysis are used in this research to monitor the non-random patterns for a multivariate process. Extracting the most important principle components from original data and monitoring those principle components by MEWMA control chart. The results show the procedure which proposed in this research has superior performance than the traditional multivariate process control methods.

並列關鍵字

non-random patterns, multivariate process control, MEWMA control chart, PCA

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