New Approximations for Reliability Integrals

A new asymptotic expansion is applied to approximate reliability integrals. The asymptotic approximation reduces the problem of evaluating a multidimensional probability integral to solving an unconstrained minimization problem. Approximations are developed in both the transformed (independently, normally distributed) variables and the original variables. In the transformed variables, the asymptotic approximation yields a very simple formula for approximating the value of the second-order reliability method integrals. In many cases, it may be computationally expensive to transform to normal variables, and an approximation using the probability distribution for the original variables can be used. Examples are presented illustrating the accuracy of the approximations, and results are compared with some existing approximations of reliability integrals.