近年來，在許多產業中，兩相依品質變數比的位置之製程監控影響產出品質，故至關重要。然而文獻上現有的研究主要集中於假設二元常態分配下兩相依變數的分配之監控。在實際應用中，我們所收集的數據往往是未知或非常態分配。因此，本研究提出了無母數和自由分配的管制圖，以在不假設特定分配的情況下監控兩相依變數比的位置。
本研究介紹了三種EWMA管制圖：一種利用Wilcoxon排序和檢定方法，另一種利用符號檢定方法，第三種則採用核密度估計方法建管制圖以監控兩相依變數比的位置。我們評估了這三種管制圖的績效並與已知多元變數分配的EWMA位置管制圖進行比較。最後，以半導體產業的數據來說明所提出的比例位置管制圖的應用。

In recent years, monitoring the location of the ratio of two correlated variables has become crucial in many industries. However, existing research on monitoring the distribution of the ratio of bivariate variables has predominantly focused on the assumption of bivariate normal variables. In practical applications, the data we collect often exhibit unknown or non-normal distributions. Hence, we propose a set of control charts, allowing us to monitor the location of the ratio of two correlated variables without assuming a specific distribution.
In this study, we introduce three EWMA control charts: one utilizing the Wilcoxon rank-sum statistic, another using the sign statistic, and the third employing the kernel density estimation method. These charts are designed to monitor the location of the ratio of two correlated variables. We evaluate the out-of-control detecting performance of the proposed charts and compare them with the exact EWMA mean charts, assuming knowledge of the distributions. Additionally, we present real data from the semiconductor industry to demonstrate the application of the proposed charts.

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