Integrating uncertainty quantification into applications increases the trustworthiness. Attributing these uncertainties to the input space elevates the trustworthiness and explainability of these systems even further. This master thesis proposes a novel method to attribute uncertainty called smoothness constrained attribution (SCA). SCA uses the uncertainty propagation mechanism and applies it to propagate the output uncertainty back to the input space with explainable artificial intelligence (XAI) methods. A framework providing synthetic data and all relevant ground truths is presented to evaluate our input uncertainty attribution mechanism (iUCAM) method and compare it to others. The iUCAMs are tested on uncertainty-aware machine learning (ML) models covering tree-based systems, neural networks ensembles, and Gaussian processes (GPs). The ML model behavior is explained using XAI methods such as averaged local effects (ALE), SmoothGrad (SG), local interpretable model-agnostic explanations (LIME), and Shapley additive explanations (SHAP). These systems are tested on various datasets, ranging from simple, nonlinear settings to more complex industrial simulations of an electric arc furnace (EAF), and, finally, on a dataset of a blast furnace. These tests show the noise robustness of XAI, uncertainty quantification (UCQ), and iUCAM, utilizing artificial heteroscedastic noise.