管制圖 (controlchart) 在工業和財務上都是常見的品質管制方法。平均串聯長度(averagerunlength,ARL)是管制圖的重要指標，它可以用來評斷一個管制圖的表現。因此計算平均串聯長度來選擇合適的管制圖是一項重要的工作。在資料是獨立的假設下，計算 ARL 是很簡單的。但現實生活中存在許多有相關性的資料，ARL 的計算就變的困難許多。我們使用copula-based 模型模擬出據有相關性的資料後，再使用蒙地卡羅模擬方法來計算不同管制圖之下的 ARL，並使用控制變異法(controlvariates) 方法以提高蒙地卡羅估計量的效率。;Control charts are commonly used for quality control in industry. The average run length (ARL) of the series is an important indicator of control charts, which can determine whether a control chart is suitable or not. Hence, calculating the ARL to select the appropriate control chart is critical. Under the assumption that the information is independently, calculating ARL is simple. But in practice data is usually dependent, and this makes the calculation of ARL challenging. We use a copula-based model to simulate the dependent data, and then use the Monte Carlo simulation method to calculate the ARL of different control charts. Furthermore, we propose a control variate method to improve the efficiency of the standard Monte Carlo estimator.
