Evaluation of Bounding Methods for Correlated Failure Modes

Introduction and Background Most engineering structures contain multiple failure modes or components in which the nonperformance of any of the events can lead to system failure. In addition, the different failure modes may be correlated due to common random variables between the events. In many cases the events are assumed independent and system failure is evaluated using unions and intersections of the events. However, neglecting correlation between events may lead to grossly over predicting the probability of failure. An upper and lower bound can be determined for the probability of system failure using first- and second-order techniques. While there is some contradiction in the literature, a complete treatment of first-order bounds is made in this research. The first- order bounds are identified for events with both positive and negative correlation. In practice the second-order bounds typically use a first-order approximation to the limit-state for each event and the intersection of the two events is estimated by the correlation between the events. For nonlinear limit-states, the bounds may not actually include the true solution based on the error of the event probabilities of failure or the predicted intersection of the events. Several numerical examples are used to evaluate the accuracy and effectiveness of