在工業製程中，管制圖是監測產品品質和檢測製成是否失控的有效工具。雖然有許多類型的管制圖可供數據分析者使用，但使用這些管制圖的前提是在變量被精確測量的情況下。然而，在實際應用中，當資料被調查者錯誤得記錄或被未經調整的機器不精確得收集時，量測誤差是無可避免的。儘管量測誤差對不同類型的管制圖的影響已經被探討過，但誤差修正的管制圖仍然很少被討論。因此在此研究中，我們提出了一種新的帶有誤差修正的變異數管制圖來填補這一研究空白。我們的主要想法是將觀察到的製程變量轉換為符號統計量，然後以一個函數來調整符號統計量，以校正量測誤差的影響。最後，我們根據修正後的符號統計量提出帶有量測誤差修正的指數加權移動平均數變異數管制圖。我們所開發的誤差修正的變異數管制圖不僅消除了量測誤差的影響，而且為監測製程變異數提供了更可靠的管制界線。透過數值分析，我們發現所提出的誤差修正變異數管制圖能夠有效處理中等和較大程度的量測誤差，並對監測製程是否失控有著良好的表現。最後，我們使用半導體資料來驗證所提出的誤差修正變異數管制圖之應用。

In industrial processes, control charts are useful tools to monitor the quality of products and detect possibly out-of-control processes. While many types of control charts have been available for data analysts, they were developed by assuming that the variables are precisely measured. In applications, however, measurement error is ubiquitous when data are falsely recorded by investigator or imprecisely collected by unadjusted machines. Even though the impacts of measurement error for different types of control charts have been explored, error-corrected control charts are still unavailable. In this study, we propose a new dispersion control chart with error correction to fill out this research gap. Our key idea is to convert the observed process variables into a flexible sign statistic, and then adopt a function to adjust the measurement error effects on the sign statistic. Finally, we develop the exponentially weight moving average dispersion control chart with measurement error correction based on the corrected sign statistic. The proposed error-corrected dispersion control chart not only eliminates measurement error effects, but also provides more reliable control limits for monitoring process dispersion. Throughout numerical examination, we find that the proposed error-corrected dispersion control chart is effective in handling the moderate and large levels of measurement error and shows well out-of-control detection performance. Finally, the proposed error-corrected dispersion control chart is implemented to the semiconductor data.

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