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Reliability-based design optimization (RBDO) problems have been intensively studied for many decades. Since Hasofer and Lind 1974, “Exact and Invariant Second-Moment Code Format,” J. Engrg. Mech. Div., 100(EM1), pp. 111–121 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, reliability analysis problems are formulated to find the reliability indices 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 is developed based on this definition. The strategies to solve RBDO problems with non-normally distributed design variables by the modified RIA are also investigated. Numerical examples using both the traditional and modified RIAs are compared and discussed. [ABSTRACT FROM AUTHOR]