First-order concepts in system reliability

The reliability of structural systems is determined by use of first-order concepts. Probability estimates for the components are calculated by linearization of the boundary of the failure domain after transforming an arbitrary vector of uncertain variables into an independent, standard normal vector. A first-order solution to the multinormal integral occurring in the formulation for elementary series or parallel systems is given and a sequence of certain probability bounds on the union of failure events involving the failure probability of any parallel subsystem and the probability of the intersection of any two or three parallel subsystems is derived. The system failure event is represented by the minimal cut set of componental failure events. The accuracy of approximations is systematically investigated and shown to be sufficient for most practical purposes. The method is illustrated with a simple example.