mcusum

**MCUSUM** is the **multivariate cumulative sum chart that accumulates directional deviation in correlated variable vectors to detect persistent process shifts** - it extends CUSUM sensitivity to multi-parameter systems. **What Is MCUSUM?** - **Definition**: Multivariate CUSUM method that tracks cumulative evidence of vector mean departure from target. - **Detection Character**: Highly sensitive to small sustained multivariate shifts. - **Model Requirements**: Needs stable covariance estimation and careful parameter tuning. - **Use Cases**: Applied in advanced SPC environments with high criticality and dense sensor data. **Why MCUSUM Matters** - **Early Multi-Signal Detection**: Captures small correlated drift that may be invisible in univariate views. - **Preventive Intervention**: Provides lead time for corrective action before specification impact appears. - **Complex-Process Fit**: Useful where interactions dominate process behavior. - **Risk Reduction**: Limits latent excursion growth across multiple process dimensions. - **Analytical Depth**: Supports rigorous surveillance of high-value manufacturing steps. **How It Is Used in Practice** - **Baseline Establishment**: Build in-control multivariate model from qualified stable periods. - **Parameter Design**: Tune reference and decision settings for target shift magnitude. - **Operational Deployment**: Use alongside T-squared or MEWMA for complementary detection coverage. MCUSUM is **a specialized but powerful multivariate SPC approach** - cumulative vector evidence enables strong sensitivity for subtle correlated process shifts.