Vein quartz often becomes the subject of chemical analysis. Laser-induced breakdown spectroscopy (LIBS) is faster, cheaper, and more environmentally friendly compared to traditional silicate analysis. This study demonstrates the feasibility of using LIBS in combination with design of experiment and chemometric methods for the classification analysis of amorphous quartz and the quantitative determination of several constant impurities. The combination of objects and methods used in this work has not been previously published. Vein quartz samples were collected from various geographically distant locations. The sample preparation for LIBS involved cutting and polishing a flat surface of the quartz specimen. The LIBS instrument settings were optimized using design of experiment method. The concentrations of several trace elements in the training and control sets of samples were determined using atomic absorption spectroscopy (AAS). The spectra and analytical data of the training set were used for multivariate calibration using Partial Least Squares Regression (PLS-R). Sample classification was performed using Principal Component Analysis (PCA). It was shown that in the score plot in the space of the first three principal components, the samples confidently group according to their sources of origin. The results were validated on a test set of samples. The accuracy of quantitative determination of Mg, Ca, Na, K, Al, Ti using LIBS exceeded 90%. A method for the quantitative determination of several elements in quartz and an approach to identifying the place of origin of a sample are proposed.

A probabilistic–deterministic design of experiments (PDDoE) approach was employed to optimize laser-induced breakdown spectroscopy (LIBS) parameters for the quantitative determination of minor components in lead-based alloys. The PDDoE optimization identified 18 J laser pump lamp energy, 1 µs delay, and 1 µs exposure as optimal conditions, minimizing spectral dispersion (5–8%) and ensuring stable plasma formation. The acquired spectra were subsequently processed in an R-based automated workflow, where Linear, Lasso, and Ridge regression models were used to establish quantitative relationships between normalized line intensities and atomic absorption spectroscopy (AAS) reference data. The resulting models demonstrated high accuracy (R² = 0.97 for Sn, 0.985 for Sb, 0.982 for Bi, 0.919 for As, and 0.905 for Ag), with prediction errors (RMSE) below 10% and limits of quantification (LOQ) under 0.05 wt.%. Principal component analysis (PCA) applied to 43 historical (19th–20th century) and technogenic samples (19th–20th century) allowed us to isolate clusters of Pb–Sb alloys corresponding to secondary accumulator materials, alongside a diffuse group of nearly pure Pb specimens containing variable minor impurities. The combined PDDoE–LIBS–R analytical framework provides a reproducible, non-destructive, and chemometrically validated methodology for the quantitative characterization and classification of archeological and industrial lead alloys.