Stochastic hybrid automata (SHA) are a powerful tool to evaluate the dependability and safety of critical infrastructures. However, the resolution of nondeterminism, which is present in many purely hybrid models, is often only implicitly considered in SHA. This paper instead proposes algorithms for computing maximum and minimum reachability probabilities for singular automata with urgent transitions and random clocks which follow arbitrary continuous probability distributions. We borrow a well-known approach from hybrid systems reachability analysis, namely flowpipe construction, which is then extended to optimize nondeterminism in the presence of random variables. Firstly, valuations of random clocks which ensure reachability of specific goal states are extracted from the computed flowpipes and secondly, reachability probabilities are computed by integrating over these valuations. We compute maximum and minimum probabilities for history-dependent prophetic and non-prophetic schedulers using set-based methods. The implementation featuring the library HyPro and the complexity of the approach are discussed in detail. Two case studies featuring nondeterministic choices show the feasibility of the approach.

随机混合自动机 (SHA) 是评估关键基础设施可靠性和安全性的强大工具。然而，许多纯混合模型中存在的非确定性的解决通常仅在 SHA 中隐式考虑。相反，本文提出了计算具有紧急情况的奇异自动机的最大和最小可达概率的算法遵循任意连续概率分布的转换和随机时钟。我们借鉴了混合系统可达性分析中的一种众所周知的方法，即流管构造，然后将其扩展到优化存在随机变量的非确定性。首先，从计算的流管中提取确保特定目标状态可达性的随机时钟的估值，其次，通过对这些估值进行积分来计算可达性概率。我们使用基于集合的方法计算依赖于历史的预言和非预言调度程序的最大和最小概率。以HyPro库为特色的实现以及该方法的复杂性进行了详细讨论。两个具有非确定性选择的案例研究表明了该方法的可行性。