Large language models (LLMs) are increasingly deployed in a wide range of applications, yet remain vulnerable to adversarial jailbreak attacks that circumvent their safety guardrails. Existing evaluation frameworks typically report binary success/failure metrics, failing to capture the temporal dynamics of how attacks succeed under persistent adversarial pressure. This preliminary work proposes a novel evaluation framework that applies survival analysis techniques to characterize LLM jailbreak vuln`erability. Our approach models the time-to-jailbreak as a survival outcome, enabling estimation of hazard functions, survival curves, and risk factors associated with successful attacks. We evaluate three LLMs against a subset of prompts from the HarmBench dataset spanning three attack categories. Our analysis reveals that models exhibit distinct vulnerability profiles: while one model demonstrates rapid degradation under iterative attacks, the two other models show consistent moderate vulnerability. Our framework provides actionable insights for model and LLM application developers and establishes survival analysis as a rigorous methodology for LLM safety evaluation.