成分資料 (Compositional Data) 係用於描述資料中各種不同組成成分之佔比情況，其具各種成分之總和為一固定常數之特性，該特性讓分析成分資料之困難度增加，目前已有學者先將成分資料利用等距對數轉換 (Isometric logratio transform) 進行轉換，並針對轉換後的資料建構管制圖來偵測具成分資料之製程是否發生偏移。然而，因偵測是針對轉換後之成分資料，除了會增加使用上的複雜性及降低可解讀性外，亦會增加計算上的成本。因在統計領域中通常會利用狄利克雷分配 (Dirichlet distribution) 來配適成分資料，故我們根據狄利克雷分配提出以計分檢定統計量 (Score test statistic) 為基礎的 MEWMA (Multivariate Exponential Weighted Moving Average) 管制圖，該方法的優點是使用時可直接對成份資料進行監控而不需要進行轉換。本研究藉由模擬研究及實例資料，對現有的方法與提出方法進行比較，結果發現本研究提出的方法對於偵測製程是否發生偏移具優異的偵測能力。另外，為了增加本研究的實用性，我們開發一套由R語言撰寫的程式，讓實務工作者在監控成分資料時使用。

Compositional data is used to describe the proportional distribution of different components. Compositional data exhibits the characteristic that the sum of its components is a fixed constant, which poses challenges for data analysis. To address this difficulty, the researcher has applied the isometric logratio transform to compositional data for constructing control charts to detect the shifts in the process. However, it is performed on the transformed compositional data, which not only increases complexity and reduces interpretability but also increases computational costs. In the field of statistics, the Dirichlet distribution is commonly employed to model compositional data. Therefore, based on the Dirichlet distribution, we propose a multivariate exponential weighted moving average (MEWMA) control chart based on the Score test statistic. An advantage of the proposed method is that it allows direct monitoring of compositional data without the need for transformation. In this study, we compare existing methods with the proposed method through simulation studies and real-world data. The results demonstrate that the proposed method exhibits excellent detection capabilities for identifying process shifts. Additionally, to enhance the practicality of our research, we developed a code written in the R programming language, which can be used by practitioners to monitor compositional data effectively.

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