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A multivariate exponentially weighted moving average (MEWMA) and Hotelling’s  T 2control charts are types of multivariate control charts for monitoring the mean vector. In this paper, we propose an efficient construction of bivariate copulas on MEWMA and Hotelling’s  T 2control charts. Observations are classified with Kendall’s tau values as weak, moderate, and strong positive dependence by using a Monte Carlo simulation to measure the average run length as a performance metric. The numerical results obtained from the simulation show that the performances of the MEWMA and Hotelling’s  T 2control charts were similar for small shifts () but the MEWMA control chart showed higher performance for moderate to large shifts.

The efficiency of constructed bivariate copulas for MEWMA and Hotelling’s T 2 control charts