Safety is an important requirement for many modern systems. To ensure safety of complex critical systems, well-known safety analysis methods have been formalized. This holds in particular for automation sytsems and transportation systems. In this paper we present the formalization of one of the most wide spread safety analysis methods: fault tree analysis (FTA). Formal FTA allows to rigorously reason about completeness of a faulty tree. This means it is possible to prove whether a certain combination of component failures is critical for system failure or not. This is a big step forward as informal reasoning on cause-consequence relations is very error-prone. We report on our experiences with a real world case study from the domain of railroads. The here presented case study is -- to our knowledge -- the first complete formal fault tree analysis for an infinite state system. Until now only finite state systems have been analyzed with formal FTA by using model checking.