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| Title: | 監控兩相依品質變數之變異數比之 EWMA 管制圖
EWMA Control Charts for Monitoring the Ratio of Variances of Two Correlated Quality Variables |
| Authors: | 周鈺宸
Chou, Yu-Chen |
| Contributors: | 楊素芬
Yang, Su-Fen
周鈺宸
Chou, Yu-Chen |
| Keywords: | 變異數比值
二元分配
管制圖
平均連串長度
Ratio of variances
bivariate distributions
control chart
average run length |
| Date: | 2024 |
| Issue Date: | 2024-09-04 14:56:47 (UTC+8) |
| Abstract: | 在統計製程管制的研究領域中，兩相依品質變數之變異數比值的追蹤 在某些實務製程中是重要的，但是文獻中尚未有見探討。因此，我們的研 究旨在探索兩相依品質變異數比的變化，以監控製程是否失控。在實務上， 製程穩定性分析、參數優化以及生產效率評估等應用，都需要追蹤變異數 比值。
在本研究中，我們分別提出兩種方法，建立不同的 EWMA 變異數比例 管制圖。第一種，我們提出使用兩相依品質變數之樣本變異數之差異之分 配建立 EWMA 變異數比例管制圖，以追蹤兩相依品質變數之母體變異數之 比。第二種方法考慮符號檢定方法(sign test method)，根據兩相依品質變 數之樣本變異數的差異是否大於其期望值，並定義指標變數分配以建立符 號管制圖。我們分別再以數值分析評估在二元常態、伽馬、偏常態母體分 配下，這兩種管制圖的管制界線與失控的偵測力。最後，我們以實際的半 導體數據驗證這兩種管制圖的應用與失控的偵測力。
In statistical process control, monitoring the ratio of variances of correlated quality variables is crucial for some practical processes. However, this topic has not been explored in literature. Our study aims to investigate the ratio of variances of two correlated quality variables to monitor whether the ratio of two variances process is out of control. In practice, monitoring the ratio of two variances is essential for process stability analysis, parameter optimization and production efficiency evaluation.
In this research, we propose two methods to establish EWMA ratio of variances control charts without the specified distributions of quality variables. The first method uses the distribution of the difference in the sample variances of two correlated quality variables to construct an EWMA ratio of variances control chart to monitor the population ratio of variances of two correlated quality variables. The second method considers the sign method to construct a sign-based control chart, where an indicator variable distribution is defined based on whether the difference in sample variances of two correlated quality variables exceeds its expected value. We conduct numerical analyses to calculate the control limits and evaluate detection capabilities of these two EWMA control charts under the bivariate normal, gamma, and skew-normal population distributions. Finally, we validate the application and detection capabilities of these two proposed control charts by using real semiconductor data. |
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| Description: | 碩士
國立政治大學
統計學系
111354021 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0111354021 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
|
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