MEWMA Chart — Multivariate EWMA Control Chart

Hotelling's T² chart applies a quadratic form directly to the current observation, giving equal weight to all past observations only implicitly through the estimated covariance. MEWMA instead applies exponential smoothing to successive vectors before computing the quadratic form, so recent observations receive higher weight and small persistent shifts accumulate over time, resulting in substantially lower ARL for detecting small mean shifts.

Lowry et al. recommend selecting λ based on the magnitude of the shift one wishes to detect quickly. Smaller values (e.g., λ = 0.05–0.10) are optimal for detecting small shifts of roughly 0.5σ or less, while larger values (λ = 0.25–0.50) perform better for moderate-to-large shifts. When the expected shift size is unknown, a common practical choice is λ = 0.10 or 0.20 paired with an ARL₀ of 200.

The chart's ARL properties are derived under multivariate normality and independence. With moderate departures from normality, performance generally remains reasonable due to smoothing, but heavy-tailed or skewed data can inflate false-alarm rates. For clearly non-normal processes, robust or nonparametric multivariate monitoring alternatives should be considered, or transformations applied before charting.