Failures in complex systems demand rapid Root Cause Analysis (RCA) to prevent cascading damage. Existing RCA methods that operate without dependency graph typically assume that the root cause having the highest anomaly score. This assumption fails when faults propagate, as a small delay at the root cause can accumulate into a much larger anomaly downstream. In this paper, we propose PRISM, a simple and efficient framework for RCA when the dependency graph is absent. We formulate a class of component-based systems under which PRISM performs RCA with theoretical guarantees. On 735 failures across 9 real-world datasets, PRISM achieves 68% Top-1 accuracy, a 258% improvement over the best baseline, while requiring only 8ms per diagnosis.