Existing benchmarks for tool-using LLM agents primarily report single-run success rates and miss reliability properties required in production. We introduce \textbf{ReliabilityBench}, a benchmark for evaluating agent reliability across three dimensions: (i) consistency under repeated execution using $\mathrm{pass}^k$, (ii) robustness to semantically equivalent task perturbations at intensity $ε$, and (iii) fault tolerance under controlled tool/API failures at intensity $λ$. ReliabilityBench contributes a unified reliability surface $R(k,ε,λ)$, \textit{action metamorphic relations} that define correctness via end-state equivalence rather than text similarity, and a chaos-engineering-style fault injection framework (timeouts, rate limits, partial responses, schema drift). We evaluate two models (Gemini 2.0 Flash, GPT-4o) and two agent architectures (ReAct, Reflexion) across four domains (scheduling, travel, customer support, e-commerce) over 1,280 episodes. Perturbations alone reduce success from 96.9% at $ε=0$ to 88.1% at $ε=0.2$. Rate limiting is the most damaging fault in ablations. ReAct is more robust than Reflexion under combined stress, and Gemini 2.0 Flash achieves comparable reliability to GPT-4o at much lower cost. ReliabilityBench provides a systematic framework for assessing production readiness of LLM agents.