The conventional fault tree and reliability analysis gives in many cases insufficient information concerning the relative frequencies of hazard events. This stems from that the basic events are not stationary and ergodic, and therefore the tolerances of the induced and top events cannot be calculated reliably based on the classical probability theory. To overcome this difficulty, the paper considers the relative frequencies of the basic events as fuzzy numbers and uses instead of probability, possible considerations for evaluating the mean values and tolerances of the top events. The possibility distribution of the basic events can be approximated based on heuristic considerations. This paper shows the use of these operators for constructing fault trees. The use of the method for numerical calculation is demonstrated on a field safety problem.