Structural and System Reliability

Chapter 9 describes simulation or sampling methods for reliability assessment. The chapter begins by describing methods for generation of pseudorandom numbers for prescribed univariate or multivariate distributions. Next, the ordinary Monte Carlo simulation (MCS) method is described. It is shown that for small failure probabilities, which is the case in most structural reliability problems, the number of samples required by MCS for a given level of accuracy is inversely proportional to the failure probability. Thus, MCS is computationally demanding for structural reliability problems. Various methods to reduce the computational demand of MCS are introduced. These include the use of antithetic variates and importance sampling. For the latter, sampling around design points and sampling in half-space are presented, the latter for a special class of problems. Other efficient sampling methods described include directional sampling, orthogonal-plane sampling, and subset simulation. For each case, expressions are derived for a measure of accuracy of the estimated failure probability. Methods are also presented for computing parameter sensitivities by sampling. Finally, a method is presented for evaluating certain multifold integrals by sampling. This method is useful in Bayesian updating, as described in Chapter 10.