factor analysis

**Factor Analysis** is a **statistical method that models observed variables as linear combinations of a smaller number of latent factors plus noise** — identifying the underlying, unobservable factors that explain the correlations among observed process variables. **How Does Factor Analysis Work?** - **Model**: $x_i = sum_j lambda_{ij} f_j + epsilon_i$ (each variable is a weighted sum of factors + unique noise). - **Factor Loadings**: $lambda_{ij}$ quantify how strongly each factor influences each variable. - **Factor Scores**: Estimated values of the latent factors for each observation. - **Rotation**: Varimax or oblique rotation makes factors more interpretable. **Why It Matters** - **Latent Structure**: Identifies hidden process factors (e.g., "thermal uniformity" driving multiple temperature readings). - **Dimensionality Reduction**: Reduces many correlated variables to a few interpretable factors. - **Unlike PCA**: Factor analysis models measurement error explicitly — better for noisy manufacturing data. **Factor Analysis** is **finding the hidden drivers** — discovering the unobservable latent factors that explain why process variables are correlated.