Lifetime analyses are crucial for ensuring the durability of new Light-emitting Diodes (LEDs) and uncertainty quantification (UQ) is necessary to quantify a lack of usable failure and degradation data. This work presents a new framework for predicting the lifetime of LEDs in terms of lumen maintenance, effectively quantifying the natural variability of lifetimes (aleatory) as well as the reducible uncertainty resulting from data scarcity (epistemic). Non-parametric survival models are employed for UQ of low-magnitude failures, while a new parametric interval prediction model (IPM) is introduced to characterize the uncertainty in high-magnitude lumen depreciation events and long-term extrapolated lifetimes. The width of interval-valued predictions reflects the inherent variability in degradation paths whilst the epistemic uncertainty, arising from data scarcity, is quantified by a statistical bound on the probability of the prediction errors for future degradation trajectories. A modified exponential flux decay model combined with the Arrhenius equation equips the IPM with physical information on the physics of LED luminous flux degradation. The framework is tested and validated on a novel database of LED degradation trajectories and in comparison to well-established probabilistic predictors. The results of this study support the validity of the proposed approach and the usefulness of the additional UQ capabilities.@en

This work investigates formal generalization error bounds that apply to support vector machines (SVMs) in realizable and agnostic learning problems. We focus on recently observed parallels between probably approximately correct (PAC)-learning bounds, such as compression and complexity-based bounds, and novel error guarantees derived within scenario theory. Scenario theory provides nonasymptotic and distributional-free error bounds for models trained by solving data-driven decision-making problems. Relevant theorems and assumptions are reviewed and discussed. We propose a numerical comparison of the tightness and effectiveness of theoretical error bounds for support vector classifiers trained on several randomized experiments from 13 real-life problems. This analysis allows for a fair comparison of different approaches from both conceptual and experimental standpoints. Based on the numerical results, we argue that the error guarantees derived from scenario theory are often tighter for realizable problems and always yield informative results, i.e., probability bounds tighter than a vacuous <inline-formula> <tex-math notation="LaTeX">$[0,1]$</tex-math> </inline-formula> interval. This work promotes scenario theory as an alternative tool for model selection, structural-risk minimization, and generalization error analysis of SVMs. In this way, we hope to bring the communities of scenario and statistical learning theory closer, so that they can benefit from each others insights.@en