Automatic Gaussian Mixture Sampling for Uncertainty Management in Circular Factories

Linear production can often approximate process uncertainty by a single Gaussian; circular manufacturing cannot. In circular manufacturing, returned parts arrive with different usage, inspection, repair, and degradation histories. As a result, product condition, process duration, and quality risk are better viewed as random variables with several condition regimes rather than as one homogeneous population. In this work, we represent this structure using Gaussian mixture models (GMMs), which combine discrete regime information and continuous variability in one probabilistic description. Many quantities needed for planning and risk assessment do not admit tractable closed-form expressions once GMM uncertainties are propagated through nonlinear engineering models or decision rules. We therefore present an automatic Monte Carlo sampling layer for GMM-based uncertainty propagation. The user specifies a tolerance and confidence level, and sampling continues until the estimated confidence interval for the selected output quantity satisfies the requested precision or the maximum sampling budget is reached. The approach enables GMM-based uncertainty models to be used in simulation-based planning, routing, inspection, and quality assessment in circular factories without manually fixing the Monte Carlo sample size in advance. ... mehrWe demonstrate the workflow with a proof of concept fatigue strength example for returned or treated metallic components. Multimodal surface state uncertainty is propagated through a nonlinear fatigue strength relation and the output is assessed by its moments and by a low strength probability.