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In solving structural reliability problems, one is often interested in evaluating the relative importance of random variables. In such an effort, random variables making relatively large contributions to the variability of the limit state function from the failure domain are generally considered as important ones. This information helps reduce the dimension and gain useful insights about the reliability problem. The first-order reliability method (FORM; Bjerager and Krenk, 1989; Ditlevsen and Madsen, 1999; Der Kiureghian, 2005) provides useful information about relative contributions of random variables through a by-product of structural reliability analysis. It is, however, noted that in some cases FORM-based importance measures are difficult to obtain or may not accurately capture the relative contribution. This is the case especially when the limit-state surface is highly complex or has multiple critical regions in the failure domain. To overcome such limitations, the authors recently proposed a generalized reliability importance measure (GRIM; Kim and Song, 2018). For this purpose, a regional participation factor is first introduced to quantify the relative importance of multiple critical regions, identified from a Gaussian mixture model representing the density in the failure domain. Such a representative Gaussian mixture can be obtained by using the cross-entropy-based adaptive importance sampling technique (Kurtz and Song, 2013). The relative importance measures obtained from the critical regions using the corresponding Gaussian densities are then combined using the regional participation factors. Through numerical examples of component and system …