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：可靠度分析是不确定性量化中的一个子领域，用于评估系统在各种不确定性下按预期运行的概率。传统上，该分析依赖于确定性模型，其试验是可重复的，即对于给定输入集，会生成一致的输出。然而，现实世界中的系统往往表现出随机行为，导致结果不可重复。这些所谓的随机模拟器，即使在固定输入下，每次运行模型时都会产生不同的输出。本文正式介绍了针对随机模型的可靠度分析，并通过使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，我们聚焦于近期引入的广义lambda模型和随机多项式混沌展开。这些仿真器旨在学习模拟器响应的固有随机性，并能够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，利用一个具有解析解的解析函数，我们证明了仿真器能够收敛到正确解。其次，我们通过一个简支梁的简单算例展示了代理模型获得的结果。最后，我们将仿真器应用于一个真实的风力涡轮机案例研究的可靠度分析，在该案例中仅有一个仿真结果数据集可用。