What is the Multivariate EWMA Chart or MEMWA Chart in R?

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The Multivariate Exponentially Weighted Moving Average (MEWMA) chart in R is a statistical process control tool used to monitor the mean vector of several correlated quality characteristics simultaneously over time. It is an extension of the univariate Exponentially Weighted Moving Average (EWMA) chart and is designed to detect small shifts in the process mean vector.

In R, the MEWMA chart is implemented using the function qcc() from the qcc package. The function takes as input a matrix of data containing the quality characteristic measurements over time, a vector of target values for each characteristic, and a covariance matrix that represents the degree of correlation between the characteristics.

The MEWMA chart plots the cumulative sum of deviations from the target values over time, weighted by the covariance matrix. A control limit is calculated based on the distribution of the cumulative sum under a hypothetical stable process. If the cumulative sum exceeds the control limit, it signals that a shift in the process mean vector has likely occurred.

The MEWMA chart is particularly useful for monitoring processes with multiple correlated quality characteristics, such as in the manufacturing of complex products. It allows for early detection of changes in the process mean vector, which can help prevent the production of defective products and improve quality control.