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政大機構典藏 > 商學院 > 統計學系 > 學位論文 > Item 140.119/136318

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/136318

Title:	以主成分分析法建立製程共變異數矩陣管制圖之研究 The Study of Covariance Matrix Control Chart Based on the Principal Component Analysis Method
Authors:	簡廷安 Chien, Ting-An
Contributors:	楊素芬 Yang, Su-Fen 簡廷安 Chien, Ting-An
Keywords:	多維度管制圖主成分分析方法符號管制圖平均連串長度維度變動調整後的管制圖偵測出異常訊息的平均時間 Adjusted average time to signal Average run length Multivariate control chart Principal component analysis Sign chart Variable dimension
Date:	2021
Issue Date:	2021-08-04 14:41:58 (UTC+8)
Abstract:	在監測製造過程中，管制圖是經常使用的手法，現今蒐集到的資料多是高維度且來自未知的分配，使得多維度且無分配假設的管制圖之研究變得更加重要。本文提出一個監控製程共變異數矩陣的管制圖，在母體分配未知或是來自非常態時，使用主成分分析方法 (PCA) 結合符號管制圖 (sign chart) 建立多元製程共變異數矩陣管制圖，並且以平均連串長度 (ARL) 做為衡量此管制圖在製程失控時的偵測能力的指標。此外，本文進一步考慮變動維度 (VD) 的想法，以減少在監測失控製程中的所需偵測時間及抽樣成本，本文採調整後的管制圖偵測出異常訊息的平均時間 (AATS) 來評估管制圖表現。本文與文獻上存在的管制圖偵測能力比較，結果發現提出的管制圖在抽樣樣本數為5且製程的共變異數或相關係數發生小幅度偏移時有較好的偵測能力，最後以半導體製程資料及礫石資料說明所提出的管制圖的應用。 The control chart is a widely used approach to monitor manufacturing processes. In the era big data, most of the collected data are high dimensional from an unknown distribution. In statistical process control (SPC), the effectiveness of univariate Shewhart control charts is challenged by monitoring highly correlated quality variables simultaneously. The development of nonparametric multivariate statistical process control (MSPC) is critically important these days. In this article, we propose a new Phase II nonparametric multivariate expone-ntially weighted moving average (EWMA) control chart for monitoring the process covariance matrix, which is based on the principal component analysis (PCA) and sign statistics. We use the average run length (ARL) to measure the detection performance of the proposed control chart. The proposed control chart surpasses the existing nonparametric control charts in some out-of-control scenarios, especially with sample size 5 and small shifts in the covariance or the correlation coefficients. The application of the proposed control is demonstrated by gravel and semiconductor process data. Further, we extend the proposed control chart by considering of variable dimension (VD) to diminish the detection time and the sampling cost under an out-of-control process. We use the adjusted average time to signal (AATS) to measure the detection efficiency of the VD control chart for various sampling plans.
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Description:	碩士國立政治大學統計學系 108354012
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0108354012
Data Type:	thesis
DOI:	10.6814/NCCU202101129
Appears in Collections:	[統計學系] 學位論文

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