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.