Safety analysis methods for safety-critical systems face new challenges as systems evolve more frequently and the interactions within systems rise in numbers and complexity. Two such challenges are: (1) the need to formally examine the impact of system interactions on safety and (2) the need to extract and readily integrate knowledge from past accidents into new systems. We propose an approach which exploits knowledge from past accidents to conduct quantitative safety analysis using interactions between system components. A case study is presented that shows how our approach provides a support mechanism to safety and design experts. Further, it shows how we identify critical interactions and their contributions to accidents. This is especially important when components have not failed but instead undesirable interactions have contributed to an accident.