RBDO problems have been intensively studied for many decades. Since Hasofer and Lind defined a measure of the second-moment reliability index, many RBDO methods utilizing the concept of reliability index have been introduced as the Reliability Index Approach (RIA). In the RIA, a reliability analysis problem is formulated to find the reliability index for each performance constraint and the solutions are used to evaluate the failure probability. However, the traditional RIA suffers from inefficiency and convergence problems. In this paper, we revisited the definition of the reliability index and revealed the convergence problem in the traditional RIA. Furthermore, a new definition of the reliability index is proposed to correct this problem and a modified Reliability Index Approach based on this definition is developed. Numerical examples using both the traditional RIA and the modified RIA are compared and discussed.

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