Industrial processes and machines pose risks in terms of equipment failure and worker accidents. In order to prevent these unwanted occurrences, the associated risks must first be analyzed. However, in traditional fault tree analysis, exact data values are used. But in real life often these values are not known precisely. There is therefore a degree of uncertainty associated with the data. Fuzzy numbers, expressed in this paper as triangular fuzzy number, provide a method for dealing and taking into account this uncertainty. In this paper, fuzzy fault tree analysis is then used. An example of a metal brake press is used to demonstrate this approach. A fault tree for a particular accident scenario is built and the fuzzy probability of occurrence of the accident under consideration is evaluated. An interesting second problem consists in starting with this value and deducing from the fault tree, what values of the occurrence probabilities of the contributing events in the fault tree minimize a function expressing the cost of work accidents. This problem is expressed mathematically and solved using a Matlab-based method over fuzzy numbers. The optimized contributing event probabilities are obtained along with the optimal cost function.