Abstract 

During the past decade, numerous endeavors have been made to develop effective reliability-based design opti-mization (RBDO) methods. Because the evaluation of probabilistic constraints defined in the RBDO formulationis the most difficult part to deal with, a number of different probabilistic design approaches have been proposed toevaluate probabilistic constraints in RBDO. In the first approach, statistical moments are approximated to evaluatethe probabilistic constraint. Thus, this is referred to as the approximate moment approach (AMA). The secondapproach, called the reliability index approach (RIA), describes the probabilistic constraint as a reliability index.Last, the performance measure approach (PMA) was proposed by converting the probability measure to a per-formance measure. A guide for selecting an appropriate method in RBDO is provided by comparing probabilisticdesign approaches for RBDO from the perspective of various numerical considerations. It has been found in theliterature that PMA is more efficient and stable than RIA in the RBDO process. It is found that PMA is accu-rate enough and stable at an allowable efficiency, whereas AMA has some difficulties in RBDO process such as asecond-order design sensitivity required for design optimization, an inaccuracy to measure a probability of failure,and numerical instability due to its inaccuracy. Consequently, PMA has several major advantages over AMA, interms of numerical accuracy, simplicity, and stability. Some numerical examples are shown to demonstrate severalnumerical observations on the three different RBDO approaches.