While quantum computers provide exciting opportunities for information processing, they currently suffer from noise during computation that is not fully understood. Incomplete noise models have led to discrepancies between quantum program success rate (SR) estimates and actual machine outcomes. For example, the estimated probability of success (ESP) is the state-of-the-art metric used to gauge quantum program performance. The ESP suffers poor prediction since it fails to account for the unique combination of circuit structure, quantum state, and quantum computer properties specific to each program execution. Thus, an urgent need exists for a systematic approach that can elucidate various noise impacts and accurately and robustly predict quantum computer success rates, emphasizing application and device scaling. In this article, we propose quantum vulnerability analysis (QVA) to systematically quantify the error impact on quantum applications and address the gap between current success rate (SR) estimators and real quantum computer results. The QVA determines the cumulative quantum vulnerability (CQV) of the target quantum computation, which quantifies the quantum error impact based on the entire algorithm applied to the target quantum machine. By evaluating the CQV with well-known benchmarks on three 27-qubit quantum computers, the CQV success estimation outperforms the estimated probability of success state-of-the-art prediction technique by achieving on average six times less relative prediction error, with best cases at 30 times, for benchmarks with a real SR rate above 0.1%. Direct application of QVA has been provided that helps researchers choose a promising compiling strategy at compile time.