Abstract. Reliability methods are probabilistic algorithms for quantifying the effect of uncertainties in simulation input on response metrics of interest. In particular, they compute approximate response function distribution statistics (probability, reliability, and response levels) based on specified probability distributions for input random variables. In this paper, recent algorithm research in first and second-order reliability methods is overviewed for both the forward reliability analysis of computing probabilities for specified response levels (the reliability index approach (RIA)) and the inverse reliability analysis of computing response levels for specified probabilities (the performance measure approach (PMA)). A number of algorithmic variations have been explored, and the effect of different limit state approximations, probability integrations, warm starting, most probable point search algorithms, and Hessian approximations is discussed. These reliability analysis capabilities provide the foundation for reliability-based design optimization (RBDO) methods, and bi-level and sequential formulations are presented. These RBDO formulations may employ analytic sensitivities of reliability metrics with respect to design variables that either augment or define distribution parameters for the uncertain variables. Relative performance of these reliability analysis and design algorithms is presented for a number of benchmark test problems using the DAKOTA software, an
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