A conformal virtual metrology framework for predictive uncertainty quantification: a full factorial experimental study of micro crown gear quality

Virtual metrology uses process data to estimate product quality before physical measurement results become available. However, most models return only a point prediction, which does not show whether an individual prediction is reliable enough for quality decisions. This paper develops a conformal prediction framework for virtual metrology of micro crown gear quality from acoustic emission signals. The framework combines regression pipelines selected for each quality characteristic with Split conformal prediction (Split CP), cross validation plus (CV+), and cross fitted conformalized quantile regression (CF-CQR). The framework is model agnostic and does not require a parametric form for the distribution of the data. Under exchangeability, conformal prediction provides finite sample marginal coverage guarantees for prediction intervals. Split CP, CV+ and CF-CQR are evaluated over repeated data partitions of the full-factorial experimental dataset using empirical coverage, interval width, and the Winkler score. The results show that acoustic emission signals support the prediction of the studied geometric characteristics, although predictive difficulty varies across targets. The conformal methods provide coverage close to the nominal level, while cross validation plus and cross fitted conformalized quantile regression generally produce more informative intervals than Split conformal prediction. The predicted intervals are used to formulate an interpretable quality assessment logic by distinguishing clear conformity, clear nonconformity, and ambiguous cases that require physical measurement or expert assessment. The proposed framework moves virtual metrology from isolated point predictions towards quality predictions that communicate uncertainty explicitly.