Structural and System Reliability

Chapter 5 presents methods for assessing structural reliability under incomplete probability information, i.e., when complete distributional information on the basic random variables is not available. First, second-moment methods are presented where the available information is limited to the means, variances, and covariances of the basic random variables. These include the mean-centered first-order second-moment (MCFOSM) method, the first-order second-moment (FOSM) method, and the generalized second-moment method. These methods lead to approximate computations of the reliability index as a measure of safety. Lack of invariance of the MCFOSM method relative to the formulation of the limit-state function is demonstrated. The FOSM method requires finding the “design point,” which is the point in a transformed standard outcome space that has minimum distance from the origin. An algorithm for finding this point is presented. Next, methods are presented that incorporate probabilistic information beyond the second moments, including knowledge of higher moments and marginal distributions. Last, a method is presented that employs the upper Chebyshev bound for any given state of probability information. The chapter ends with a discussion of the historical significance of the above methods as well as their shortcomings and argues that they should no longer be used in practice.