近年來，在工業製造過程中同時監控兩個上的相關品質變數非常重要，因此多元統計過程控制 (MSPC) 成為研究人員的熱門研究領域。由於許多數據資料不服從多元常態分佈，因此無分配假設的管制圖更是一個相當重要的工具來監控產品品質。
本文建構了兩種新的指數加權移動平均 (EWMA) 管制圖。一種是基於Hotelling T^2二次式來監控資料服從多元常態分佈的共變異數矩陣。另一個則是結合資料深度 (data depth) 和符號方法 (sign method) 的無分佈假設的管制圖來監控過程的分散程度。此外，我們添加了變動維度 (VD) 技巧來建構新的變動維度的管制圖，用於監控過程具有 s_2 個變量的共變異數矩陣。在 s_2 個變量中，其中一些衡量容易或只需要較少的測量成本，而其餘的變量衡量困難或需要昂貴的測量成本。
當共變異矩陣的變異數有變化時，所提出的管制圖比文獻中現有的管制圖表現更好。此外，我們通過使用半導體數據說明了所提出的管制圖的應用。因此，我們建議採用提出的管制圖來檢測過程分散的變化。

Today it is important to monitor more than two correlated quality variables at the same time in the industrial manufacturing process, so the multivariate statistical process control (MSPC) becomes a popular research area for the researchers. Since many data do not follow a multivariate normal distribution, the study of distribution-free control chart is very important.
This paper constructs two kinds of new exponentially weighted moving average (EWMA) control charts. One is based on the Hotelling T^2 quadratic form to monitor the covariance matrix for a process following a multivariate normal distribution. Another is a distribution-free control chart based on the data depth and the sign method to monitor process dispersion. In addition, we add the technique of variable dimension (VD) to build new VD-type control charts for monitoring covariance matrix of a process with s_2 variables. Some of them are easy or need less cost to measure and the remaining variables are difficult or need expensive cost to measure.
The proposed control charts performs better than the existing control charts in literature when the covariance matrix has changes in variances. Furthermore, we illustrate the application of the proposed control charts by using the semiconductor data. Hence, we suggest adopting the proposed control charts to detect the shifts in process dispersion.

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