Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments are repeatable, i.e., they produce consistent outputs for a given set of inputs. However, real-world systems often exhibit stochastic behavior, leading to non-repeatable outcomes. These so-called stochastic simulators produce different outputs each time the model is run, even with fixed inputs. This paper formally introduces reliability analysis for stochastic models and addresses it by using suitable surrogate models to lower its typically high computational cost. Specifically, we focus on the recently introduced generalized lambda models and stochastic polynomial chaos expansions. These emulators are designed to learn the inherent randomness of the simulator's response and enable efficient uncertainty quantification at a much lower cost than traditional Monte Carlo simulation. We validate our methodology through three case studies. First, using an analytical function with a closed-form solution, we demonstrate that the emulators converge to the correct solution. Second, we present results obtained from the surrogates using a toy example of a simply supported beam. Finally, we apply the emulators to perform reliability analysis on a realistic wind turbine case study, where only a dataset of simulation results is available.

翻译：可靠性分析是不确定性量化领域的一个分支，旨在评估系统在各种不确定性条件下按预期运行的概率。传统上，该分析依赖于确定性模型，其中实验具有可重复性，即对于给定输入集能产生一致的输出。然而，实际系统常表现出随机特性，导致结果不可重复。这类所谓的随机模拟器即使在输入固定的情况下，每次运行模型也会产生不同的输出。本文正式引入针对随机模型的可靠性分析方法，并通过采用合适的代理模型来降低其通常较高的计算成本。具体而言，我们聚焦于近期提出的广义λ模型与随机多项式混沌展开方法。这些代理模型旨在学习模拟器响应固有的随机性，并能以远低于传统蒙特卡洛模拟的成本实现高效的不确定性量化。我们通过三个案例研究验证了所提方法：首先，利用具有解析解的数学函数证明代理模型能够收敛至正确解；其次，通过简支梁的示例模型展示基于代理模型的量化结果；最后，将代理模型应用于实际风力涡轮机的可靠性分析案例，该案例中仅存在仿真结果的数据集。