The Performance of the MEWMA Control Chart when Parameters are Estimated

Abstract

In the present article, we study the effect of estimating the vector of means and variance-covariance matrix in the performance of the multivariate exponentially weighted moving average (MEWMA) control chart. We show through simulation that the performance of the MEWMA control chart is affected when the parameters are estimated compared to the known parameters case. We show also that larger number of Phase I samples are required to achieve the expected statistical performance of the MEWMA chart when smaller smoothing constants are used in designing it. Under some sampling scenarios, more than 2,500 samples are needed to estimate the unknown parameters to satisfy the intended statistical performance. The control limit that achieves the desired in control ARL when estimating the parameters is computed in several cases and formulas used to find approximately its values are given. Finally, an optimal design strategy for the MEWMA chart with estimated parameters is presented.

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