Large Language Models (LLMs) are increasingly deployed across diverse domains, raising the need for rigorous reliability assessment methods. Existing benchmark-based evaluations primarily offer descriptive statistics of model accuracy over datasets, providing limited insight into the probabilistic behavior of LLMs under real operational conditions. This paper introduces HIP-LLM, a Hierarchical Imprecise Probability framework for modeling and inferring LLM reliability. Building upon the foundations of software reliability engineering, HIP-LLM defines LLM reliability as the probability of failure-free operation over a specified number of future tasks under a given Operational Profile (OP). HIP-LLM represents dependencies across (sub-)domains hierarchically, enabling multi-level inference from subdomain to system-level reliability. HIP-LLM embeds imprecise priors to capture epistemic uncertainty and incorporates OPs to reflect usage contexts. It derives posterior reliability envelopes that quantify uncertainty across priors and data. Experiments on multiple benchmark datasets demonstrate that HIP-LLM offers a more accurate and standardized reliability characterization than existing benchmark and state-of-the-art approaches. A publicly accessible repository of HIP-LLM is provided.