ABSTRACT
Within the broader field of reliability theory, the class of time-invariant structural reliability problems is characterized by an n-vector of basic (directly observable) random variables and a subset
Ω of their outcome space, which defines the “failure” event. The probability of failure, , is given by an n-fold integral
(14.1)
where f(x) is the joint probability density function (PDF) of x. This problem is challenging because for most nontrivial selections of f(x) and
Ω , no closed form solution of the integral exists. Furthermore, straightforward numerical integration is impractical when the number of random variables, n, is greater than 2 or 3. Over the past two decades, a number of methods have been developed to compute this probability integral. This chapter introduces two of the most widely used methods: the first-order reliability method, FORM, and the second-order reliability method, SORM. Extensions of the above formulation to time-or space-variant problems and to applications involving finite element analysis are also described in this chapter.
