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| Title: | 以符號檢定為基的多元比例管制圖
A multidimensional ratios control chart based on the sign test |
| Authors: | 鄭智忠
Cheng, Chih-Chung |
| Contributors: | 楊素芬
葉百堯
Yang, Su-Fen
Yeh, Arthur
鄭智忠
Cheng, Chih-Chung |
| Keywords: | 多維度管制圖
平均值比
符號檢定
平均連串長度
Average run length
Multidimensional ratios of means
Multivariate control chart
Sign test |
| Date: | 2022 |
| Issue Date: | 2022-09-02 14:46:00 (UTC+8) |
| Abstract: | 在製程監控的領域中，管制圖是常見且有效的方法。
在許多產業中，如玻璃工業、化學工業以及食品業等行業，追蹤相關的製程變數平均值比或是成分間平均值的比例是個重要的課題。過去關於監控平均值比的管制圖研究，多集中於二元常態變數的平均值比，多維度平均值比之管制圖尚未被探討。
本研究提出一個可以監控各種分配多維度平均值比之管制圖。本文將符號檢定（sign test）的方法應用於多維度平均值比的監控，建立一個可以適用於各種分配的多維度平均值比管制圖，並以平均連串長度（ARL）做為衡量管制圖偵測失控製程的能力指標。我們發現此管制圖的偵測能力在相關係數大、變異係數小以及樣本數大時偵測能力較佳；在不同的失控分配中，數據分析顯示此管制圖在多元均勻分配下製程的偵測能力表現最佳，而在多元非中心t分配下製程的偵測能力表現最差。此管制圖在各種分配下的具有相似的管制界限，因此可以將管制界限取平均值，而建立一致的管制界限。此外，建立此管制圖的管制界限只需決定每組抽樣樣本數以及管制圖的加權常數即可。最後以牛奶成份資料說明所提出的多維度平均值比管制圖的應用。
In the manufacturing processes monitoring, control chart is a widely used and effective approach. Monitoring the multidimensional ratios of the means among correlated process variables or ingredients of a product is important in many industries, such as glass industry, chemistry industry and food industry. However, existing studies about the single ratio of means control chart all focus on bivariate normal variables. Thus, we are motivated to develop a new control chart for monitoring multidimensional ratios of means of correlated variables under any distributions.
In this article, we apply a sign test approach to monitor the multidimensional ratios of means, by constructing a distribution-free multidimensional ratios of means control chart. We use the average run length (ARL) to measure the detection performance of the proposed control chart. We find that the proposed control chart has good detection performance with large correlation coefficient, small coefficient of variation, and large sample size. Numerical analyses show that the proposed chart has the best detection performance under multivariate uniform distribution, and the worst detection performance under multivariate noncentral t distribution. The proposed chart has similar control limits under different distributions, hence, a unified control limit can be obtained by taking the average of the control limits. The unified control limit of the proposed control chart could be obtained given only the group sample size and the smoothing parameter for any distributed correlated quality variables. Data of the ingredients of milk are presented to demonstrate the application of the proposed multidimensional ratios of means control chart. |
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| Description: | 碩士
國立政治大學
統計學系
109354012 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109354012 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU202201157 |
| Appears in Collections: | [統計學系] 學位論文
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