A tail-adjusted reliability index for non-Gaussian structural systems

The conventional reliability index, although commonly adopted in structural engineering, is constructed under Gaussian assumptions and remains largely insensitive to distributional tail characteristics. As a result, it may significantly underestimate the probability of failure when input variables exhibit heavy-tailed or asymmetric behavior. To overcome this limitation, this study introduces a new reliability metric, referred to as the Tail-Adjusted Reliability Index (TARI), which incorporates not only the first and second moments, but also the skewness, excess kurtosis, and tail index of the safety margin distribution. The formulation is based on a combination of the Cornish–Fisher expansion for moment-based corrections and the Generalized Pareto Distribution from extreme value theory for explicit tail modeling. The proposed approach is verified using Monte Carlo simulations applied to structural systems with Gaussian and non-Gaussian resistance and load variables. Three representative case studies are analyzed, covering distributions such as Weibull, Gamma, and Gumbel, where TARI consistently reduces the reliability index by 16–31%, even in systems calibrated to have identical classical indices. These reductions confirm that TARI captures risk contributions from non-Gaussian tails that are neglected by traditional methods. The results suggest that applying TARI can support the development of more conservative design factors, especially relevant in code calibration under uncertain environmental loads, fatigue-sensitive applications, and material degradation scenarios.