###### Abstract  
Remaining useful life (RUL) prediction is central to prognostics and reliability assessment of light-emitting diode (LED) systems. Their unknown long-term service life remaining when subject to specific operating conditions is affected by various sources of uncertainty stemming from production of individual system components, application of the whole system, measurement and operation. To enhance the reliability of model-based predictions, it is essential to account for all of these uncertainties in a systematic manner. This paper proposes a Bayesian hierarchical modelling framework for inverse uncertainty quantification (UQ) in LED operation under thermal loading. The main focus is on the LED systems' operational thermal resistances, which are subject to system and application variability. Posterior inference is based on a Markov chain Monte Carlo (MCMC) sampling scheme using the Metropolis-Hastings (MH) algorithm. Performance of the method is investigated for simulated data, which allow to focus on different UQ aspects in applications. Findings from an application scenario in which the impact of disregarded uncertainty on RUL prediction is discussed highlight the need for a comprehensive UQ to allow for reliable predictions. LED system; uncertainty quantification; remaining useful life; thermal resistance; power cycling; Bayesian hierarchical modelling; test data simulation; MCMC +
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acceleration factor is the temperature change during the on-/off-cycle. Power cycling can lead to thermal fatigue of interconnection technologies such as wire-bonds [5] and solder joints [9]. Solder joint fatigue leads to embrittlement, which in turn increases the thermal resistance. If the thermal resistance, and thus the temperature of the LED system, exceeds a certain threshold, the LED cannot serve its original purpose and needs to be replaced [10]. These acceleration factors are used to build corresponding lifetime models for LEDs. The accuracy of such lifetime prediction models describing the relationship between testing condition and resulting service life crucially depends on various sources of uncertainty. Examples include production uncertainty in device parameters, e.g., the porosity of the die attach or solder interfaces; uncertainty resulting from application, such as mounting on a heat sink via thermal interface materials; measurement noise; uncertainty in initial conditions (e.g., in input parameters of lifetime models); operating uncertainty in the experimental conditions, affecting the accuracy of the equipment used for testing or measuring; or statistical estimation uncertainty. The literature categorizes uncertainty in three dimensions, cf., e.g., [11; 12]: the location of uncertainty, which refers to different sources of uncertainty underlying the system in focus (e.g., production, application, measurement or operation); its levels, ranging from complete knowledge to total ignorance; and last, its nature, i.e., the differentiation between two different types of uncertainty, namely aleatory variability and epistemic uncertainty. _Aleatory_ variability refers to the (natural) intrinsic randomness in any process or model parameter, and _epistemic_ uncertainty results from lack of knowledge or ignorance. Epistemic uncertainty includes parametric and model uncertainty due to imperfect knowledge about parameters and the process of interest. With increased knowledge in the form of more data or the use of more refined models, epistemic uncertainty is reducible in practice, whereas the stochastic component is not; cf. [13; 14]. In general, uncertainty quantification (UQ) refers to the process of identifying, characterizing, representing and quantifying all sources of uncertainty within an application to enhance the reliability of model-based predictions and to allow for decision-making at a known level of confidence [15; 16]. This is also a key issue in prognostics and health management (PHM), especially in prognostics [17; 18].