Physically Unclonable Functions (PUFs) are a promising hardware security primitive for AI-powered Cyber-Physical Systems (AI-CPS), offering low-cost, low-area, tamper-resistant, and unique key generation. However, the lack of a standardized methodology and lack of consensus in PUF performance metric definition does not allow for fair comparisons across designs which can impact their confidence in use for security. This paper presents a systematic analysis methodology for evaluating PUFs at the circuit simulation level. The methodology establishes transient Monte Carlo simulation strategies, structured data extraction and processing, and metric computation. It addresses the nuanced simulation requirements for each performance metric—uniqueness, repeatability, identifiability, reliability, and randomness—ensuring that each is accurately and fairly assessed. A practical explanation using an Arbiter PUF in Cadence® is provided, along with data handling and metric calculation examples in Python. The proposed methodology facilitates reproducibility and comparability across PUF designs.