A Double Multivariate Exponentially Weighted Moving Average (dMEWMA) Control Chart for a Process Location Monitoring

Abstract

A new control scheme, dMEWMA, for detecting shifts in the mean vector of multivariately normally distributed quality characteristics is presented. It is shown that the ARL performance of dMEWMA depends on the mean and variance-covariance matricies only through the non-centrality parameter value. Through Monte Carlo simulations, the performance of dMEWMA for detecting various shifts is compared to the competing control schemes, MEWMA and Hotelling's χ². It is concluded that dMEWMA outperforms MEWMA and Hotelling's χ² control schemes for small and larger shifts. In comparison to MEWMA control schemes, dMEWMA schemes are optimal for larger values of the smoothing parameter λ and perform much better for very small shifts in the process mean. Finally, an example to illustrate the construction of the dMEWMA control scheme is introduced.

Keywords:

• Average run length (ARL)
• Double EWMA
• Hotelling's T²
• Multivariate EWMA
• Statistical process control

Mathematics Subject Classification:

• 62P30

Notes

*Out-of-control signal.