Stochastic Digital Twin Frameworks for Uncertainty Quantification in Industrial Operations

Industrial digital twins increasingly support monitoring, simulation, optimization, and decision-making across manufacturing, energy systems, logistics, infrastructure, and quality control. However, many implementations still depend on deterministic assumptions that treat system inputs, model parameters, and operating conditions as fixed. This limits their reliability in real industrial environments where uncertainty arises from sensor noise, demand fluctuation, machine degradation, environmental variability, model abstraction, and supply chain disruption. This review synthesizes stochastic digital twin frameworks for uncertainty quantification in industrial operations. It examines how aleatory, epistemic, data-quality, model, and prediction uncertainties enter digital twin pipelines and propagate through virtual models into operational decisions. The review evaluates key modelling and computational approaches, including Bayesian updating, Monte Carlo simulation, stochastic processes, Markov models, polynomial chaos expansion, Gaussian process emulators, probabilistic machine learning, reduced-order models, and hybrid physics-data architectures. It also maps major industrial applications in predictive maintenance, production scheduling, supply chain risk management, energy optimization, and process quality control. The analysis shows that stochastic digital twins improve decision quality by replacing single-point predictions with probability distributions, confidence bounds, failure probabilities, risk metrics, and scenario-sensitive outputs. Yet practical deployment remains constrained by computational cost, data quality, calibration difficulty, real-time latency, multi-level integration, and lack of standardized implementation protocols. Future progress requires adaptive learning, uncertainty-aware artificial intelligence, scalable distributed computing, and interoperable digital twin ecosystems. Stochastic digital twins will not eliminate industrial uncertainty, but they can make it measurable, interpretable, and actionable for resilient industrial decision-making.