Bounds on the Probability of Failure in Random Vibration

A new method to construct upper and lower bounds for the failure probability of a structure exposed to random excitations is presented. The method is based on an extension of the classical inclusion-exclusion series of Rice where the main idea is to take into consideration only realizations which are in the safe area at a number of previous instants of time. By a numerical example it is demonstrated that this method may lead to rather sharp bounds.