## 2 Related Work  
Bayesian methods are appealing for addressing system reliability problems due to their natural incorporation of prior knowledge at various levels of complex systems into the analysis; see, e.g., [26]. Increasing complexity of component dependencies, failure modes and causes has led to an increasing need for flexible modelling frameworks in reliability analysis. Bayesian hierarchical modelling has become more and more popular in this field with applications in very different areas; examples include railway maintenance [27], reliability of wheel wears [28], Li-ion batteries [29] or wind turbines [30]. Attractiveness of BHM is related to its modelling capability of complex strutures, its natural ability to characterize and analyse uncertainty as well as its ability to integrate information from different sources, including experimental and historical data, or prior expert opinion. This is particularly useful for the reliability analysis of systems comprising sparse data, where failures in test operations are used as the main source of information for system evaluation, if at all. Data-driven approaches are widely used for RUL prediction; see, e.g., [31; 32]; and specifically, in the field of LEDs [33; 34; 35; 36; 37]. Advances in computational capabilities have also contributed to the popularity of Bayesian methods in this field [38]. [PERSON] and [PERSON] [39] and [PERSON] et al. [40] use particle-filter-based approaches based on Sequential Monte Carlo (SMC) techniques to predict lumen maintenance of LED light sources. In [PERSON] et al. [41], a Bayesian regression model is developed to predict luminous flux degradation in LED lamps. [PERSON] et al. [42] propose a Bayesian method to estimate RUL considering measurement uncertainty for high-power white LED packages and lamps. In these studies, RUL prediction is based on lumen degradation of LED systems, which refers to the decrease in light output in the course of aging. In contrast, LED degradation in [PERSON] et al. [43] is directly addressed by analysing the increasing junction temperature change over time. There, a regression-based approach using Bayesian additive models for location, scale and shape (BAMLSS) [44] is proposed to model thermal LED degradation, handling the epistemic uncertainty in unknown model parameters. The concept of Bayesian hierarchical modelling for UQ in inverse problems within engineering applications has already been proposed by [PERSON] and [PERSON] [24]. The authors have demonstrated its suitability for modelling physical systems in the presence of epistemic uncertainty and aleatory variability using simulated data of simply supported beam deflections. Pursuing their approach in the context of LEDs allows for comprehensive consideration of potential sources of uncertainty in LED operation under thermal loading and represents a new contribution to the development of methods for modelling LED degradation with improved reliability. Bayesian frameworks are a well-established and popular modelling choice for UQ in inverse problems; beyond their natural mechanism for regularization, they account for randomness and uncertainty in a systematic manner; cf. [45]. As an alternative, forward uncertainty propagation methods and complementary sensitivity analysis tackle the aleatory variability in parameters by studying the impact of uncertain input parameters on system response uncertainty; see, e.g., [16]. Monte Carlo simulation techniques (see, e.g., [46]) are standard and versatile methods in this field; however, they suffer from the \"lack of input uncertainty information\" issue and low efficiency, especially in complex engineering problems. Surrogate models such as polynomial chaos expansions and Gaussian process regression thus have become a popular alternative tool for uncertainty propagation, being computationally much cheaper to evaluate, see, e.g., [47]. Further non-probabilistic approaches to handle epistemic uncertainty include fuzzy set theory, interval theory and (Dempster-Shafer) evidence theory [48; 49].