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研究生:胡逢升
論文名稱:建立管制區域來同時監控製程的位置與離散
論文名稱(外文):Design of a Control Region for Monitoring Joint Location and Dispersion
指導教授:楊素芬楊素芬引用關係
指導教授(外文):Yang, Su Fen
學位類別:碩士
校院名稱:國立政治大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
畢業學年度:103
語文別:英文
論文頁數:60
中文關鍵詞:控制區域不受分配限制核密度估計方法同時監控製程
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  • 被引用被引用:0
  • 點閱點閱:73
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  • 收藏至我的研究室書目清單書目收藏:0
不論在製造流程或是在服務流程上,管制圖是一個能夠監督流程失控的非常有效工具。現今社會中,在製造流程與服務流程上,資料大多來自非常態分佈或是未知的分佈,以至於最為人所常用且建立在常態分配假設下的舒華特管制圖不適用於此。此文章中,我們提出了一個使用核密度估計方法(kernel density estimation approach)來建構出一個不受分配限制的中位數與四分位差控制區域,以同時監控製程的位置與離散程度。平均連串長度(ARL)是用以測量管制圖的失控偵測能力。在此文章中,比較了我們所提出來的控制區域與文獻上其他無母數管制圖的偵測製程失控能力。數值分析顯示我們所提出的中位數與四分位數的控制區域在同時監測位置與離散的能力較好。文章中亦提出運用此控制區域的例子,最後則為本文章的總結。
Control charts are effective tools for monitoring quality of manufacturing processes and service processes. Nowadays, much of the data in service or manufacturing industries comes from processes having non-normal distributions or unknown distributions. The commonly used Shewhart mean and variable control charts, which depend heavily on the normality assumption, are not appropriately used here. In this article, we propose a distribution-free control region of the median and IQR using the kernel density estimation methods to simultaneously monitor the location and dispersion of an unknown underlying continuous distribution. Furthermore, the average run lengths (ARL) of the proposed control region is used to measure the out-of-control detection performance. The performance of the proposed control region and some other non-parametric charts for detecting out-of-control location and scale are compared. The proposed control region of the median and IQR shows as well or better detection performance compared to existing non-parametric control charts that can simultaneously monitor the location and scale. Numerical examples illustrate the application of the proposed control region. Summary and conclusions are offered.
1. Introduction 1
2. Determination of the True Control Region of the Median and IQR for the Quality Variable with a Specified Distribution 3
2.1 Design of a median control chart 3
2.2 Design of an IQR control chart 4
2.3 Design of the control region of the median and IQR 5
2.3.1 Determination of the control region of the median and IQR using the joint CDF of the median and IQR 6
2.3.2 Determination of the control region of the median and IQR using joint pdf of the median and IQR 7
2.4 Performance measurement of the control region of the median and IQR 11
3. Determination of the Control Region of the Median and IQR for the Quality Variable with Unknown Distribution – the Kernel Density Estimation Method 15
3.1 Using the kernel density estimation method to estimate the pdf of the distribution-free process data 15
3.2 Determination of the approximated control region using the kernel density estimation method 17
3.2.1 Determining the control region using the one-dimensional kernel density estimation method 17
3.2.2 Determining the control region using the two-dimensional kernel density estimation method 19
3.3 Performance measurement of the control region of the median and IQR 19
4. Design the K Control Chart for Monitoring Joint Location and Dispersion 29
4.1 Design the K control chart using the one-dimensional kernel density estimation method 29
4.2 Design the K control chart using the two-dimensional kernel density estimation method 30
5. Performance Comparison 30
6. Real Examples 38
6.1 TSMC Company’s stock price data 38
6.1.1 Control region of the median and IQR of TSMC company’s stock price using the kernel density estimation method 41
6.1.2 The K control chart 44
6.2 Service Times Data 49
6.2.1 Control region of the median and IQR of service times data using the kernel density estimation method 49
6.2.2 The K control chart 53
6.2.3 Performance comparison of the proposed control charts 55
7. Summary and Concluding Remarks 57
Reference 58

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