t-squared chart

**T-squared chart** is the **multivariate SPC chart based on Hotelling T-squared statistic to monitor joint deviation from a multivariable process center** - it compresses correlated variable behavior into one anomaly indicator. **What Is T-squared chart?** - **Definition**: Chart of covariance-scaled distance between each observation vector and the in-control mean vector. - **Mathematical Role**: Accounts for variable correlation so normal co-movement is not falsely flagged. - **Signal Output**: Produces a single statistic with control limit for multivariate out-of-control detection. - **Deployment Scope**: Common in equipment health monitoring and advanced process-control environments. **Why T-squared chart Matters** - **Joint Fault Detection**: Finds abnormal combinations that single-parameter charts may miss. - **Dimensionality Reduction**: Simplifies high-dimensional monitoring into actionable alarm logic. - **False-Alarm Control**: Correlation-aware scaling improves signal quality in coupled systems. - **Operational Speed**: One composite index enables faster frontline decisioning. - **Quality Safeguard**: Early multivariate anomaly detection limits excursion propagation. **How It Is Used in Practice** - **Baseline Modeling**: Estimate mean vector and covariance from stable reference operation. - **Limit Setting**: Define control threshold by confidence level and sample context. - **Contribution Analysis**: Decompose alarm events to identify dominant variable drivers. T-squared chart is **a core multivariate SPC instrument for correlated-process monitoring** - covariance-aware anomaly scoring improves detection coverage in complex manufacturing systems.