Ensemble-based uncertainty quantification of virtual measurements in multi-stage battery production in relation to measurement uncertainty

Battery production consists of tightly interconnected process steps, yet physical inspections are performed only at selected points due to cost and time constraints, causing late scrap detection and unnecessary resource use. With increasing data availability, virtual measurements can predict quality from process data without additional inspection effort. However, existing approaches lack uncertainty quantification comparable with measurement uncertainty and compatible with established metrological standards, while remaining flexible in algorithm choice. This paper proposes a framework for virtual measurements in multistage production, enabling quality prediction at each process step and quality propagation between consecutive process steps. Uncertainty is quantified using ensemble methods, interpreted as an empirical measurement model combined with a Monte Carlo approach, enabling uncertainty estimates comparable to the GUM and allowing existing standards for conformity assessment and test process capability to be applied. By providing uncertainty-aware virtual measurements at every production step, the framework enables early, standards-compliant quality decisions without additional physical inspections. The framework is validated on 1,000 synthetic battery modules across three production steps. The best virtual measurement achieves R 2 = 0.87 at the stacking stage, with a total uncertainty of 0.030 W versus a reference of 0.024 W, demonstrating uncertainty-aware forecasting and avoidance of overconfident decisions.